Question

1st semester practice test
multiple choice
identify the choice that best completes the statement or answers the question.

1. which of the following is not the graph of a function?

a. b. c. d.

1. the table shows how much jan charges to rent bouncy castles for birthday parties. she charges a fixed fee plus an hourly rate after the first three hours.

jan’s bouncy castles
hours rented: 3, 4, 5, 6, 7
amount charged: $225, $275, $325, $375, $425
what is jan’s hourly rate after the first three hours?
a. $112.50 per hour b. $225.00 per hour c. $75.00 per hour d. $50.00 per hour

1. what values for x satisfy the inequality 10x - 4 > 6?

a. x < 1 b. x > 1 c. x < \\(\frac{1}{5}\\) d. x > \\(\frac{1}{5}\\)

Explanation:

Question 1:

Step1: Recall the vertical line test

A graph is a function if any vertical line drawn intersects the graph at most once.

Step2: Analyze each graph

• Graph a: A vertical line (e.g., \(x = 3\)) would intersect the graph multiple times (it's a vertical line itself), so it fails the vertical line test.
• Graph b: Passes vertical line test (parabola opening downward, each \(x\) has one \(y\)).
• Graph c: Passes vertical line test (horizontal line, each \(x\) has one \(y\)).
• Graph d: Passes vertical line test (parabola opening upward, each \(x\) has one \(y\)).

Step1: Identify the change in hours and cost

After 3 hours, at 4 hours cost is \$275, at 5 hours \$325, etc. The change in hours from 3 to 4 is \(4 - 3=1\) hour, change in cost is \(275 - 225 = 50\) dollars.

Step2: Confirm the hourly rate

Check another interval: from 4 to 5 hours, cost changes from \$275 to \$325, difference is \(325 - 275 = 50\) dollars for 1 hour. So the hourly rate after 3 hours is \$50 per hour.

Step1: Solve the inequality \(10x - 4>6\)

Add 4 to both sides: \(10x - 4+ 4>6 + 4\) → \(10x>10\)

Step2: Divide by 10

Divide both sides by 10: \(\frac{10x}{10}>\frac{10}{10}\) → \(x > 1\)

Answer:

a. The graph in option a (the vertical line - like graph)

Question 2: