DEAMER C UNIT 1 REVIEW SUMMATIVE 26 QUESTIONS (4/14/2026)

$x$	$k(x)$
0	4
1	5
2	4
3	1
4	−4

1

The table shows values for a function $k$ at selected values of $x$. Which of the following claim and explanation statements best fit these data?

$k$ is best modeled by a linear function, because the rate of change over consecutive equal-length input-value intervals is constant.

$k$ is best modeled by a linear function, because the change in the average rates of change over consecutive equal-length input-value intervals is constant.

$k$ is best modeled by a quadratic function, because the rate of change over consecutive equal-length input-value intervals is constant.

$k$ is best modeled by a quadratic function, because the change in the average rates of change over consecutive equal-length input-value intervals is constant.

1

Let $g_n$ represent a geometric sequence where $g_3 = 8$ and $g_5 = 2$. What is the value of $g_8$?

$-7$

$\dfrac{1}{2}$

$\dfrac{1}{4}$

$\dfrac{1}{8}$

1

The figure shows a circle centered at the origin with an angle of measure $\theta$ in standard position. The terminal ray of the angle intersects the circle at point $S$. The coordinates of $P$ are $(12,5)$ and the radius of the circle is $13$. What is the value of $\sin \theta$?

$\sin \theta = \dfrac{12}{13}$

$\sin \theta = \dfrac{5}{13}$

$\sin \theta = -\dfrac{12}{13}$

$\sin \theta = -\dfrac{5}{13}$

1

In the $xy$-plane, the graph of a rational function $f$ has a hole at $x = -3$ and a vertical asymptote at $x = 2$. Which of the following could be an expression for $f(x)$?

$\dfrac{x+3}{x-2}$

$\dfrac{x-3}{(x-3)(x+2)}$

$\dfrac{(x+3)(x-2)^3}{(x+3)^2(x-2)^2}$

$\dfrac{(x+3)^3(x-2)}{(x+3)^2(x-2)^2}$

1

The table below gives selected values for the function $h$.
$x$
1
2
3
4
5
$h(x)$
824
330
132
53
21
Which of the following graphs could represent these data in a semi-log plot, where the vertical axis is logarithmically scaled?
(A)
(B)
(C)
(D)

Graph A

Graph B

Graph C

Graph D

1

Where both expressions are defined, which of the following is equivalent to $\dfrac{\sin(2x)\cdot\tan x}{\csc x}$?

$- \sin^4 x$

$2 \sin x$

$2 \sin^3 x$

$(\sin^2 x)(\tan x)$

1

A group of students wanted to see if there is a relationship between the number of students absent on a given day and the time of year. The students estimated the number of students that were absent over a period of time. Then, the students developed a linear regression model for the number of absences over time. The figure shows a graph of the residuals of the linear regression. Which of the following statements about the linear regression is true?

The linear model is not appropriate, because there is no apparent pattern in the graph of the residuals.

The linear model is not appropriate, because the graph of the residuals has more points below $0$ than above $0$.

The linear model is appropriate, because there is no apparent pattern in the graph of the residuals.

The linear model is appropriate, because the absolute values of the residuals are all less than $1$.

1

The figure shows the graph of the sinusoidal function $f(x) = a \cos\left(\frac{1}{2}x\right) + d$ in the $xy$-plane, where $a$ and $d$ are constants. Which of the following gives the value of $a \cdot d$?

$-12$

$-8$

$12$

$16$

1

A

B

C

D

1

Which of the following functions has two vertical asymptotes, one horizontal asymptote, and no holes?

$f(x) = \dfrac{(x - 2)^2 (x - 6)^3}{(x + 1)(x - 4)^2}$

$f(x) = \dfrac{(x - 2)^2 (x - 6)}{(x + 1)(x - 4)^2}$

$f(x) = \dfrac{(x - 2)^2 (x - 6)}{(x^2 - 1)(x - 4)}$

$f(x) = \dfrac{(x - 2)^2 (x - 6)}{(x^2 - 1)(x^2 - 4)}$

1

Given that the function $g(x) = (5x + 3)^2(x - 5)(x - 3)^k$ has its end behavior defined by $\lim_{x \to -\infty} g(x) = \infty$ and $\lim_{x \to \infty} g(x) = \infty$, which value of $k$ would satisfy the end behavior condition for the function?

$0$

$1$

$4$

$6$

1

Suppose that the function $h(x) = (x^2 + k)(x - 3)^2(x + 5)$ has two imaginary roots with integer coefficients. What value(s) of $k$ would satisfy these conditions?

$2i$

$2i$ and $-2i$

$4$

$4$ and $-4$

1

What is the coefficient of $x$ in the expansion of $(2x + 5)^3$?

$150$

$84$

$60$

$40$

1

Let $h(x) = -2x^{2}(x+2)(x-3)$. What are all the intervals for which $f(x) > 0$?

$(-2,3)$

$(-2,0)$ and $(0,3)$

$(-\infty,-2)$ and $(0,3)$

$(-\infty,-2)$ and $(3,\infty)$

1

$x$
$k(x)$
$0$
$1$
$3$
$7$
$6$
$10$
$9$
$12$
Selected values of the polynomial $k$ are shown in the table above. Which of the following claim and explanation statements could be true about $k(x)$?

The graph of $k$ could be concave up because the average rates of change over consecutive equal-length input-value intervals are positive.

The graph of $k$ could be concave up because the average rates of change over consecutive equal-length input-value intervals are increasing.

The graph of $k$ could be concave down because the average rates of change over consecutive equal-length input-value intervals are decreasing.

The graph of $k$ could be concave down because the average rates of change over consecutive equal-length input-value intervals are negative.

1

Let $f(x)=\dfrac{(x+4)^3(x-2)^2(x-5)^2}{(x+4)^2(x-5)^3}$. The graph of $f$ has a zero at which of the following values of $x$?

$x=-4$ only

$x=2$ only

$x=-4$ and $x=5$ only

$x=-4$, $x=2$ and $x=5$

1

The rational function $r$ is given by $r(x)=\dfrac{2x^{2}-13x+30}{x-3}$. Which of the following statements about $r$ is correct?

The graph of $r$ has a horizontal asymptote at $y=2$.

The graph of $r$ has a slant asymptote of $y=2x+19$.

The graph of $r$ has a slant asymptote of $y=2x+9$.

The graph of $r$ has a slant asymptote of $y=2x-7$.

1

Let $f(x) = x^{2} + 8x + 4$ and $g(x) = 2x^{2} + 5x - 6$. Find all intervals on which $g(x) \ge f(x)$.

$[-2, 5]$

$[5, \infty)$

$[-2, 5] \cup \left[\dfrac{5}{4}, \infty \right)$

$(-\infty, -2] \cup [5, \infty)$

1

Let $h$ be a polynomial function whose graph has a point of inflection at $x = 4$. Which of the following statements about $h$ must be true?

The graph of the rate of change of $h$ has a zero that will cross the $x$-axis at $x = 4$.

The graph of the rate of change of $h$ has a relative extremum at $x = 4$.

The graph of $h$ has a relative extremum at $x = 4$.

The graph of $h$ is tangent to the $x$-axis at $x = 4$.

1

The function $y = f(x)$ has a domain of $-7 \le x \le 12$ and a range of $-3 \le y \le 6$. The graph of $y = g(x)$ is the result of the transformation $g(x) = f(x + 3) - 4$. Which of the following gives the domain of $g(x)$?

$-11 \le x \le 8$

$-10 \le x \le 9$

$-4 \le x \le 15$

$-8 \le x \le 11$

1

LEAVE ANSWERS IN EXACT FORM

1

DEAMER C UNIT 1 REVIEW SUMMATIVE 26 QUESTIONS (4/14/2026)

The table shows values for a function $k$ at selected values of $x$. Which of the following claim and explanation statements best fit these data?

Let $g_n$ represent a geometric sequence where $g_3 = 8$ and $g_5 = 2$. What is the value of $g_8$?

The figure shows a circle centered at the origin with an angle of measure $\theta$ in standard position. The terminal ray of the angle intersects the circle at point $S$. The coordinates of $P$ are $(12,5)$ and the radius of the circle is $13$. What is the value of $\sin \theta$?

In the $xy$-plane, the graph of a rational function $f$ has a hole at $x = -3$ and a vertical asymptote at $x = 2$. Which of the following could be an expression for $f(x)$?

The table below gives selected values for the function $h$.$x$12345$h(x)$8243301325321Which of the following graphs could represent these data in a semi-log plot, where the vertical axis is logarithmically scaled?(A)(B)(C)(D)

Where both expressions are defined, which of the following is equivalent to $\dfrac{\sin(2x)\cdot\tan x}{\csc x}$?

The figure shows the graph of the sinusoidal function $f(x) = a \cos\left(\frac{1}{2}x\right) + d$ in the $xy$-plane, where $a$ and $d$ are constants. Which of the following gives the value of $a \cdot d$?

Which of the following functions has two vertical asymptotes, one horizontal asymptote, and no holes?

Given that the function $g(x) = (5x + 3)^2(x - 5)(x - 3)^k$ has its end behavior defined by $\lim_{x \to -\infty} g(x) = \infty$ and $\lim_{x \to \infty} g(x) = \infty$, which value of $k$ would satisfy the end behavior condition for the function?

Suppose that the function $h(x) = (x^2 + k)(x - 3)^2(x + 5)$ has two imaginary roots with integer coefficients. What value(s) of $k$ would satisfy these conditions?

What is the coefficient of $x$ in the expansion of $(2x + 5)^3$?

Let $h(x) = -2x^{2}(x+2)(x-3)$. What are all the intervals for which $f(x) > 0$?

$x$$k(x)$$0$$1$$3$$7$$6$$10$$9$$12$Selected values of the polynomial $k$ are shown in the table above. Which of the following claim and explanation statements could be true about $k(x)$?

Let $f(x)=\dfrac{(x+4)^3(x-2)^2(x-5)^2}{(x+4)^2(x-5)^3}$. The graph of $f$ has a zero at which of the following values of $x$?

The rational function $r$ is given by $r(x)=\dfrac{2x^{2}-13x+30}{x-3}$. Which of the following statements about $r$ is correct?

Let $f(x) = x^{2} + 8x + 4$ and $g(x) = 2x^{2} + 5x - 6$. Find all intervals on which $g(x) \ge f(x)$.

Let $h$ be a polynomial function whose graph has a point of inflection at $x = 4$. Which of the following statements about $h$ must be true?

The function $y = f(x)$ has a domain of $-7 \le x \le 12$ and a range of $-3 \le y \le 6$. The graph of $y = g(x)$ is the result of the transformation $g(x) = f(x + 3) - 4$. Which of the following gives the domain of $g(x)$?

LEAVE ANSWERS IN EXACT FORM

The table shows values for a function $k$ at selected values of $x$. Which of the following claim and explanation statements best fit these data?

Let $g_n$ represent a geometric sequence where $g_3 = 8$ and $g_5 = 2$. What is the value of $g_8$?

The figure shows a circle centered at the origin with an angle of measure $\theta$ in standard position. The terminal ray of the angle intersects the circle at point $S$. The coordinates of $P$ are $(12,5)$ and the radius of the circle is $13$. What is the value of $\sin \theta$?

In the $xy$-plane, the graph of a rational function $f$ has a hole at $x = -3$ and a vertical asymptote at $x = 2$. Which of the following could be an expression for $f(x)$?

The table below gives selected values for the function $h$.$x$12345$h(x)$8243301325321Which of the following graphs could represent these data in a semi-log plot, where the vertical axis is logarithmically scaled?(A)(B)(C)(D)

Where both expressions are defined, which of the following is equivalent to $\dfrac{\sin(2x)\cdot\tan x}{\csc x}$?

The figure shows the graph of the sinusoidal function $f(x) = a \cos\left(\frac{1}{2}x\right) + d$ in the $xy$-plane, where $a$ and $d$ are constants. Which of the following gives the value of $a \cdot d$?

Which of the following functions has two vertical asymptotes, one horizontal asymptote, and no holes?

Given that the function $g(x) = (5x + 3)^2(x - 5)(x - 3)^k$ has its end behavior defined by $\lim_{x \to -\infty} g(x) = \infty$ and $\lim_{x \to \infty} g(x) = \infty$, which value of $k$ would satisfy the end behavior condition for the function?

Suppose that the function $h(x) = (x^2 + k)(x - 3)^2(x + 5)$ has two imaginary roots with integer coefficients. What value(s) of $k$ would satisfy these conditions?

What is the coefficient of $x$ in the expansion of $(2x + 5)^3$?

Let $h(x) = -2x^{2}(x+2)(x-3)$. What are all the intervals for which $f(x) > 0$?

$x$$k(x)$$0$$1$$3$$7$$6$$10$$9$$12$Selected values of the polynomial $k$ are shown in the table above. Which of the following claim and explanation statements could be true about $k(x)$?

Let $f(x)=\dfrac{(x+4)^3(x-2)^2(x-5)^2}{(x+4)^2(x-5)^3}$. The graph of $f$ has a zero at which of the following values of $x$?

The rational function $r$ is given by $r(x)=\dfrac{2x^{2}-13x+30}{x-3}$. Which of the following statements about $r$ is correct?

Let $f(x) = x^{2} + 8x + 4$ and $g(x) = 2x^{2} + 5x - 6$. Find all intervals on which $g(x) \ge f(x)$.

Let $h$ be a polynomial function whose graph has a point of inflection at $x = 4$. Which of the following statements about $h$ must be true?

The function $y = f(x)$ has a domain of $-7 \le x \le 12$ and a range of $-3 \le y \le 6$. The graph of $y = g(x)$ is the result of the transformation $g(x) = f(x + 3) - 4$. Which of the following gives the domain of $g(x)$?

LEAVE ANSWERS IN EXACT FORM

The table below gives selected values for the function $h$.
$x$
1
2
3
4
5
$h(x)$
824
330
132
53
21
Which of the following graphs could represent these data in a semi-log plot, where the vertical axis is logarithmically scaled?
(A)
(B)
(C)
(D)

$x$
$k(x)$
$0$
$1$
$3$
$7$
$6$
$10$
$9$
$12$
Selected values of the polynomial $k$ are shown in the table above. Which of the following claim and explanation statements could be true about $k(x)$?

The table below gives selected values for the function $h$.
$x$
1
2
3
4
5
$h(x)$
824
330
132
53
21
Which of the following graphs could represent these data in a semi-log plot, where the vertical axis is logarithmically scaled?
(A)
(B)
(C)
(D)

$x$
$k(x)$
$0$
$1$
$3$
$7$
$6$
$10$
$9$
$12$
Selected values of the polynomial $k$ are shown in the table above. Which of the following claim and explanation statements could be true about $k(x)$?