IM 3 Semester 1 Final 2024

Identify the equation of the graph below.

Which of the following could be that of the graph below?

Which of the following graphs are shifted 2 units Right and 3 units Down from the Parent function. Choose all that apply

Which of the following denotes the equation of the transformed function if f(x)=x^3 is translated

A. 4 units right

B. Reflected about the x-axis(flipped) and

C. Has a vertical stretch of 3

Graph each equation then answer the question. Which transformation BEST describes the translation FROM f(x)=-2|x+1|+4 TO g(x)=-2|x+4|-1

Sketch

Which of the following is true about f(x) ?

I. The domain is (-\infty, \infty )?

II. The range is (-\infty, 3)?

III. There is a Relative Minimum of 1 at x=3

Selected values of the temperature, H, of an alloy, in degrees Celsius, are given below at t minutes. Find the average rate of change of the temperature, H(t), between t = 4 minutes and t = 12 minutes. Write the formula first

The profits of a startup company can be modeled by the function, P(t)=\sqrt{5t+1} where P(t) is measured in millions of dollars, and t is years since 2000. Find the Average Rate of Change of Profits between t=3 and t=7 . Write the formula first.

If f(x)=2x^{2}-3x+5, find the value of f(3).

Make sure to show your work for full credit.

Graph

and label the Critical Point. State the Increasing and Decreasing Interval of

Examine EACH choice carefully.

Use the graph of f(x) and g(x) below.

Solve: f(x)=g(x).

What are the intervals for which the function below is Decreasing?

What are the intervals for which the function below is INCREASING?

Use the function below to solve f(x)<0

Which of the points below are x-intercepts and the y-intercepts of f(x)? Drag the points that belong in each category

Find the Maximum or the Minimum value of

Use the graph below to answer question a and b

a. Find f(-2)=

b. Solve f(x)=3.

Graph

Which of the following is the Domain and Range of f(x)?

If f(x)=2x^{2}-3x+1 and g(x) =x+1 find f(g(x))

Solve f(x)<g(x) with f(x) being the line and g(x) being the parabola

If f(x) and g(x) are shown below, find the value of f(g(8))

If f(x)=2x^{2}-x+5 and g(x)=3x-5 find f(g(1))

For the piecewise function

Find the value of f(-2)

Solve the system of equations below hint: use substitution

Show work. Don't skip steps!

Find the Rate of Change of the line passing through the points

Show work.

Write the equation of the line below in Standard form:

Make sure to show your work.

Find the x-intercept and y-intercept of the line below, then graph the function in the show your work section.

Given a system of equation below:

Find the point of intersection

Which of the following is the equation of the line through (4,-3) and perpendicular to the line

y=3x+2

Which of the graphs below represent the solution to the system of Inequalities:

Show work.

Solve for the x-intercepts

Find the zeros of

Find the x-value of the point of intersection of

Find the x-intercepts of

Solving the equation

is equivalent to finding the roots of which of the following?

Factor:

Expand

A portion of the graph is shown below. Observing its x-intercepts and vertex which of the following could be the function?

Which of the following function has zeros

Find the x-intercepts of

Which of the following could be the equation below?

For what value(s) of x is 4x(2x-18) equal to zero?

Factor