Q: Which of the following is the correct piecewise definition for the function whose graph is shown above?

$$f(x) = \begin{cases} -\frac{1}{2}x^2$ & \text{if } x \u003c 1 \\ 2x + 1 & \text{if } x \geq 1 \end{cases}$$

Q: Which of the following best describes the end behavior of the function as $$x \to -\infty$$?

$$f(x) \to -\infty ($$since the quadratic dominates for $$x \u003c 1)$$

Question 1

Given the graph above, which of the following best describes the range of the function $$f(x)$$?

Accepted Answer

$$(-\infty, 0] \cup [3, \infty)$$

Question 2

Which of the following is the correct piecewise definition for the function whose graph is shown above?

Accepted Answer

$$f(x) = \begin{cases} -\frac{1}{2}x^2$ & 	ext{if } x \u003c 1 \ 2x + 1 & 	ext{if } x \geq 1 \end{cases}$$

Question 3

At which $$x-$$value does the function transition from a quadratic to a linear expression in the graph above?

Accepted Answer

$$x = 1$$

Question 4

Which of the following statements is true about the continuity of the function shown in the graph above?

Accepted Answer

The function is continuous for all real numbers.

Question 5

What is the value of $$f(1)$$ for the function shown in the graph above?

Accepted Answer

$$3$$

Question 6

Which of the following best describes the end behavior of the function as $$x 	o -\infty$$?

Accepted Answer

$$f(x) 	o -\infty ($$since the quadratic dominates for $$x \u003c 1)$$

Question 7

For $$x \geq 1$$, what is the slope of the function shown in the graph above?

Accepted Answer

$$2$$

Question 8

Which of the following intervals is NOT included in the range of the function shown in the graph above?

Accepted Answer

$$(0, 3)$$

Question 9

If the function $$f(x) is $$defined as in the graph above, which of the following statements is true?

Accepted Answer

$$f(x) is $$not one-to-one.

Question 10

Suppose the function in the graph above models the height (in meters) of a projectile for $$x \u003c 1$$ and the height of a rising elevator for $$x \geq 1. $$What is the minimum possible height according to the model?

Accepted Answer

$$0$$

Analyzing a Piecewise Function and Its Range

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