B UNIT 1 REVIEW SUMMATIVE

1

The figure shows a graph of the polynomial function $f$ in the $xy$-plane. Which of the following could be an expression for $f(x)$?

$3(x+2)(x-4)$

$-3(x+2)(x-4)$

$-3(x+2)^2(x-4)$

$-3(x+2)(x-4)^2$

1

For $x > 0$, which of the following is equivalent to $\ln(x+3) - 2\ln x - \ln(x+4)$?

$\ln\bigl(x^2(x+3)(x+4)\bigr)$

$\ln\left(\dfrac{x+3}{2x(x+4)}\right)$

$\ln\left(\dfrac{x+3}{x^2(x+4)}\right)$

$\ln\left(\dfrac{(x+3)(x+4)}{x^2}\right)$

1

The location of a point in the plane is given by polar coordinates $\left(5,\dfrac{7\pi}{6}\right)$. Which of the following gives another representation for this point in polar coordinates?

$\left(-5,-\dfrac{5\pi}{6}\right)$, because $\dfrac{5\pi}{6}$ clockwise from the positive $x$-axis lies in the opposite direction of $\dfrac{7\pi}{6}$, and the radius is negative.

$\left(-5,-\dfrac{11\pi}{6}\right)$, because $\dfrac{11\pi}{6}$ clockwise from the positive $x$-axis lies in the opposite direction of $\dfrac{7\pi}{6}$, and the radius is negative.

$\left(5,\dfrac{\pi}{6}\right)$, because $\dfrac{\pi}{6}$ counterclockwise from the positive $x$-axis lies on the same line as $\dfrac{7\pi}{6}$, and the radius is positive.

$\left(5,\dfrac{5\pi}{6}\right)$, because $\dfrac{5\pi}{6}$ counterclockwise from the positive $x$-axis lies on the same line as $\dfrac{7\pi}{6}$, and the radius is positive.

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 polynomial function $p$ is given by $p(x) = -x^{2}(x-2)(x+3)$. What are all intervals on which $p(x) < 0$?

$(-3, 0)$

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

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

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

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

B UNIT 1 REVIEW SUMMATIVE

The figure shows a graph of the polynomial function $f$ in the $xy$-plane. Which of the following could be an expression for $f(x)$?

For $x > 0$, which of the following is equivalent to $\ln(x+3) - 2\ln x - \ln(x+4)$?

The location of a point in the plane is given by polar coordinates $\left(5,\dfrac{7\pi}{6}\right)$. Which of the following gives another representation for this point in polar coordinates?

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 $\dfrac{\sin(2x)\cdot\tan x}{\csc x}$?

A polynomial function $p$ is given by $p(x) = -x^{2}(x-2)(x+3)$. What are all intervals on which $p(x) < 0$?

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 $a \cdot d$?

The figure shows a graph of the polynomial function $f$ in the $xy$-plane. Which of the following could be an expression for $f(x)$?

For $x > 0$, which of the following is equivalent to $\ln(x+3) - 2\ln x - \ln(x+4)$?

The location of a point in the plane is given by polar coordinates $\left(5,\dfrac{7\pi}{6}\right)$. Which of the following gives another representation for this point in polar coordinates?

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 $\dfrac{\sin(2x)\cdot\tan x}{\csc x}$?

A polynomial function $p$ is given by $p(x) = -x^{2}(x-2)(x+3)$. What are all intervals on which $p(x) < 0$?

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 $a \cdot d$?

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)

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)