$$30 \times 3 + 0.15 \times 200 = \120$

Question 1

Which of the following correspondences is NOT a function from $$A = \{1, 2, 3\} to$$ $$B = \{a, b, c\}$$?

Accepted Answer

$$f(1) = a,\ f(2) = b,\ f(2) = c$$

Question 2

Given the function $$f(x) = 2x^2$ - 3x + 5$$, what is $$f(-2)$$?

Accepted Answer

$$f(-2) = 19$$

Question 3

Find the slope and $$y-$$intercept of the line given by $$3x - 2y = 6.$$

Accepted Answer

Slope $$= \dfrac{3}{2}$$, $$y-$$intercept $$= -3$$

Question 4

A line passes through the point $$(4, -1)$$ and has slope $$m = 2. $$What is its equation in point-slope form and in slope-intercept form?

Accepted Answer

Point-slope: $$y + 1 = 2(x - 4)$$; Slope-intercept: $$y = 2x - 9$$

Question 5

Given points $$A(2, 5)$$ and $$B(-4, -7)$$, find the slope of the line through $$A$$ and $$B.$$

Accepted Answer

Slope $$= 2$$

Question 6

A company charges a flat fee of \$$50 plus \20 $$per hour for consulting. Which equation models the total cost $$C$$ for $$h$$ hours?

Accepted Answer

$$C = 20h + 50$$

Question 7

A car rental company charges \$$30 per day plus \0.15 $$per mile driven. If you rent a car for 3 days and drive 200 miles, what is the total cost?

Accepted Answer

$$30 	imes 3 + 0.15 	imes 200 = \120$

Question 8

Which of the following is the graph of $$y = x^2$ - 4$$?

Accepted Answer

A parabola opening upwards with vertex at $$(0, -4)$$

Question 9

For the quadratic function $$f(x) = -x^2$ + 6x - 5$$, what are the coordinates of the vertex?

Accepted Answer

$$(3, 4)$$

Question 10

Solve the quadratic equation $$x^2 - 5x + 6 = 0$.

Accepted Answer

$$x = 2,\ x = 3$$

Question 11

Simplify the exponential expression $$\$$left(2x^3$$\$$right)^4$$.

Accepted Answer

$$16x^{12}$$

Question 12

Convert $$x^{1/3} to $$radical notation.

Accepted Answer

$$\sqrt[3]{x}$$

Question 13

Rewrite $$\sqrt[4]{x^3$} as an $$expression with rational exponents.

Accepted Answer

$$x^{3/4}$$

Question 14

Determine the domain of the function $$f(x) = \sqrt{x - 2}.$$

Accepted Answer

$$[2, \infty)$$

Question 15

A ball is thrown upward and its height after $$t$$ seconds is given by $$h(t) = -16t^2$ + 64t + 80. $$What is the maximum height reached by the ball?

Accepted Answer

$$208$$ feet

Question 16

Given the data set: $$(1, 2), (2, 4), (3, 8), (4, 16)$$, which type of function best models the data?

Accepted Answer

Exponential function

Question 17

Which of the following is NOT a possible $$y-$$intercept for the line passing through $$(2, 5)$$ with slope $$-3$$?

Accepted Answer

$$(0, 1)$$

Question 18

If $$f(x) = x^2$ - 4x + 3$$, for which value(s) of $$x$$ does $$f(x) = 0$$?

Accepted Answer

$$x = 1 or$$ $$x = 3$$

Question 19

Which of the following best describes the line $$y = 7$$?

Accepted Answer

A horizontal line with slope $$0$$

Step-by-Step Guidance for Precalculus and Calculus Foundations

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