Question

consider this table of values.
input 0 1 2 3
output 0 2 4 6
which of these graphs corresponds to the function shown in the table of values?
(graphs w, x, y, z are shown)
a. z
b. y
c. x
d. w

Explanation:

Step1: Analyze the table

The table has inputs (x) 0, 1, 2, 3 and outputs (y) 0, 2, 4, 6. The slope \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{2 - 0}{1 - 0}=2 \), so the equation is \( y = 2x \).

Step2: Check the graphs

• For \( x = 1 \), \( y = 2 \); \( x = 3 \), \( y = 6 \).
• Graph Z: When \( x = 1 \), \( y\approx2 \); \( x = 3 \), \( y\approx6 \), and the slope is 2 (steeper, since \( y = 2x \) has slope 2).
• Graphs W, X, Y: Their slopes or points don't match \( y = 2x \) as closely as Z.

Answer:

A. Z