Question 1

Which of the following is the correct graph for the function $$y = -x^2$ + 4$$?

Accepted Answer

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

Question 2

Given the linear equation $$4x - 6y = 18$$, what is the $$y-$$intercept?

Accepted Answer

$$y = -3$$

Question 3

Solve for $$x in $$the equation $$\frac{7}{25}x = 3 + \frac{5}{5}.$$

Accepted Answer

$$x = 75$$

Question 4

A store charges $$2.50$$ for the first page and $$0.65$$ for each additional page to fax. The total price $$P$$ for faxing $$x$$ pages is given by $$P = 0.65(x - 1) + 2.50. $$How many pages can be faxed for $$8.35$$?

Accepted Answer

$$11$$ pages

Question 5

Given $$x^2 + 10x - 24 = 0$, what are the solutions using the quadratic formula?

Accepted Answer

$$\{12, -2\}$$

Question 6

Compute the discriminant for $$x^2 - 12x + 36 = 0$ and determine the number and type of solutions.

Accepted Answer

$$0$$; one real solution

Question 7

Solve the polynomial equation $$x^3$$ - $$8x^2 + 15x = 0$ by factoring and using the zero product principle.

Accepted Answer

$$\{0, 3, 5\}$$

Question 8

Solve and check the equation $$(x + 8)(x^2$) = 216.$$

Accepted Answer

$$\{6, -6\}$$

Question 9

Divide and express the result in standard form: $$\frac{9}{4} \div \frac{3}{8}.$$

Accepted Answer

$$6$$

Question 10

Solve the absolute value inequality $$|x - 3| \u003c 3$$ and express the solution set in interval notation.

Accepted Answer

$$(0, 6)$$

Question 11

Find the product and write the result in standard form: $$(5x + 1)(5x - 5).$$

Accepted Answer

Question 12

Solve for $$x in $$the equation $$5(x + 2) \leq 4(x - 1) + x$$ and express the solution set in interval notation.

Accepted Answer

$$(-\infty, 4]$$

Question 13

Given the formula $$A = \frac{2A - bh}{h}$$, solve for $$A in $$terms of $$b$$ and $$h.$$

Accepted Answer

Question 14

If $$y = -4x + 7$$, what is the slope and $$y-$$intercept of the line?

Accepted Answer

Slope: $$-4$$, $$y-$$intercept: $$7$$

Question 15

A wealthy grandparent invests $$25,000$$ for a grandchild, with $$x$$ dollars at $$4\%$$ and the rest at $$10\%$$ annual interest. If the total interest after one year is $$1,600$$, how much was invested at $$4\%$$?

Accepted Answer

$$10,000 at$$ $$4\%$$

Question 16

Solve the equation by completing the square: $$x^2 + 10x - 21 = 0$.

Accepted Answer

$$\{7, -3\}$$

Question 17

Which of the following intervals represents the solution to $$x \u003e 5$$?

Accepted Answer

$$(5, \infty)$$

Question 18

Given the function $$y = x^2$ + 3$$, what is the vertex of the parabola?

Accepted Answer

$$(0, 3)$$

Question 19

If $$f(x) = 2x + 1$$ and $$g(x) = x^2$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$9$$

Question 20

Which of the following best describes the solution set for $$x^2$$ \u003c 9$$?

Accepted Answer

$$(-3, 3)$$

Precalculus Study Guide: Functions, Equations, and Inequalities

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