Question 1

Which of the following best describes the slope-intercept form of a linear function?

Accepted Answer

$$f(x) = mx + b$$

Question 2

Given the linear function $$f(x) = 3x + 5$$, what is the slope $$m$$?

Accepted Answer

$$m = 3$$

Question 3

If the slope $$m of a $$linear function is negative, what is the behavior of $$f(x)$$ over its domain?

Accepted Answer

It decreases left-right over domain.

Question 4

A company buys a new computer for $$2100 and depreciates it using the straight-line method over 3 years. What is the slope m$ of the value function?

Accepted Answer

$$m = -700$$

Question 5

Which of the following is NOT a property of linear functions?

Accepted Answer

Rate of change varies

Question 6

Given $$f(x) = 3x + 5$$ and $$g(x) = -2x + 15$$, solve $$f(x) = g(x). $$What is $$x$$?

Accepted Answer

$$x = 3$$

Question 7

What is the implied domain of the function $$V(x)$$ representing the value of a computer depreciating over 3 years?

Accepted Answer

$$0 \leq x \leq 3$$

Question 8

For the quadratic function $$f(x) = ax^2$ + bx + c$$, why must $$a 
eq 0$$?

Accepted Answer

To ensure the graph is a parabola

Question 9

Given the quadratic function $$f(x) = x^2$ - 2x - 15$$, what is the vertex $$(h, k)$$?

Accepted Answer

$$(1, -16)$$

Question 10

For the quadratic function $$f(x) = ax^2$ + bx + c$$, what is the formula for the axis of symmetry?

Accepted Answer

$$x = -\frac{b}{2a}$$

Question 11

A rectangular field is to be enclosed with 2000 feet of fencing along three sides. What is the maximum area that can be enclosed?

Accepted Answer

$$500,000 sq ft$

Question 12

Given the demand equation $$x = -7p + 140$$, $$0 \leq p \leq 20$$, what is the revenue function $$R in $$terms of $$x$$?

Accepted Answer

$$R(x) = -\frac{1}{7}x^2$ + 20x$$

Question 13

For the revenue function $$R(x) = -\frac{1}{7}x^2$ + 20x$$, what quantity $$x$$ maximizes revenue?

Accepted Answer

$$x = 70$$

Question 14

For the function $$f(x) = x^2$ - 2x - 15$$, what is the domain?

Accepted Answer

$$x \in \mathbb{R}$$

Question 15

For the function $$f(x) = x^2$ - 2x - 15$$, what is the range?

Accepted Answer

$$y \in [-16, \infty)$$

Question 16

A suspension bridge has towers 1200 meters apart and cables form a parabola. If the towers are 85 meters above the roadway, what is the height of the cables at a point 300 meters from the center?

Accepted Answer

$$h = 70$$

Question 17

For the quadratic function $$f(x) = a(x-h)^2$ + k$$, what does $$(h, k)$$ represent?

Accepted Answer

The vertex

Question 18

If a company wants to earn at least $$525 in revenue, for R(x$$) = -\frac{1}{7}$$x^2 + 20x$, what values of x$ should they consider?

Accepted Answer

$$x \in [21, 49]$$

Question 19

Which form is best for identifying the vertex of a quadratic function?

Accepted Answer

Vertex form $$a(x-h)^2 + k$

College Algebra Unit 2: Linear and Quadratic Functions (Sections 4.1, 4.3, 4.4)

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