CHSPE Algebra 5

Question 1

What is the domain of the function f(x) = √(x - 3)?

Accepted Answer

x ≥ 3

Answer

The expression under the square root must be ≥ 0, so x - 3 ≥ 0, meaning x ≥ 3.

Question 2

A store marks up items by 40%. If the original cost is c, which expression represents the selling price?

Accepted Answer

1.4c

Answer

The selling price is original cost plus 40% of cost = c + 0.4c = 1.4c.

Question 3

Which of the following pairs of lines are perpendicular?

Accepted Answer

y = ½x + 4 and y = -2x + 1

Answer

Perpendicular slopes are negative reciprocals; ½ and -2 are negative reciprocals (½ × -2 = -1).

Question 4

Simplify: 3√12 - √27

Accepted Answer

3√3

Answer

3√12 = 3(2√3) = 6√3 and √27 = 3√3, so 6√3 - 3√3 = 3√3.

Question 5

The graph of y = x² is shifted 3 units to the right. What is the new equation?

Accepted Answer

y = (x - 3)²

Answer

A horizontal shift right by 3 units replaces x with (x - 3), giving y = (x - 3)².

California High School Proficiency Exam Practice Test