Question 1

Which of the following best describes the graph of the function $$f(x) = x^2$?

Accepted Answer

A parabola opening upwards with vertex at $$(0,0)$$

Question 2

What is the range of the function $$f(x) = x^2$?

Accepted Answer

$$[0, \infty)$$

Question 3

Which of the following statements is true about the function $$y = |x|$$?

Accepted Answer

It is an even function symmetric about the $$y-$$axis

Question 4

What is the $$y-$$intercept of the function $$y = -\frac{1}{2}x + 2$$?

Accepted Answer

$$2$$

Question 5

Which of the following best describes the slope of the line $$y = -\frac{1}{2}x + 2$$?

Accepted Answer

The slope is $$-\frac{1}{2}$$ and the line falls to the right

Question 6

If $$f(x) = x^2$, what is f(-3$$)$$?

Accepted Answer

$$9$$

Question 7

For the function $$y = |x|$$, which of the following points lies on its graph?

Accepted Answer

$$(-3, 3)$$

Question 8

A company models its profit $$P (in $$thousands of dollars) as a function of time $$t (in $$years) by $$P(t) = t^2$. What does this model suggest about the company's profit over time?

Accepted Answer

Profit increases at an increasing rate as time increases

Question 9

Which transformation occurs when the function $$f(x) = x^2$ is changed to f(x$$) = $$(x-3)^2$$?

Accepted Answer

The graph shifts 3 units to the right

Question 10

A medical researcher models the dosage $$D (in mg) of a $$drug as a function of time $$t (in $$hours) by $$D(t) = |t-4|. $$What is the minimum dosage, and at what time does it occur?

Accepted Answer

Minimum dosage is $$0 mg at$$ $$t = 4$$ hours

Question 11

Which of the following is the equation of a line parallel to $$y = -\frac{1}{2}x + 2$$ and passing through the point $$(0, -3)$$?

Accepted Answer

$$y = -\frac{1}{2}x - 3$$

Question 12

If $$y = |x|$$ models the distance from a point to the origin on a number line, what is the distance when $$x = -7$$?

Accepted Answer

$$7$$

Question 13

Which of the following best describes the domain of $$y = -\frac{1}{2}x + 2$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 14

A ball is thrown upward and its height $$h (in $$meters) after $$t$$ seconds is modeled by $$h(t) = -5t^2$ + 20t. $$What type of function is this, and what is the shape of its graph?

Accepted Answer

Quadratic; parabola opening downwards

Question 15

Which of the following represents the reflection of $$f(x) = x^2$ over the x$-axis?

Accepted Answer

$$f(x) = -x^2$

Question 16

If the function $$y = -\frac{1}{2}x + 2$$ models the cost (in dollars) to produce $$x$$ units of a product, what happens to the cost as the number of units increases?

Accepted Answer

The cost decreases

Fundamental Functions in Precalculus: Quadratic, Absolute Value, and Linear Functions

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