Question

1. consider the three functions.

function 1 has a graph, function 2 is $y = x^2 - 3$, function 3 has a table with x and y values (-4,1), (-2,2), (0,3), (2,4).
which statement is true?
a function 1 is the only linear function.
b function 1, function 2, and function 3 are all nonlinear functions.
c function 1 and function 3 are the only linear functions.
d function 2 and function 3 are the only nonlinear functions.

Explanation:

Step1: Identify linearity of Function 1

A straight line graph means it is linear, following the form $y=mx+b$.

Step2: Identify linearity of Function 2

The function $y=x^2-3$ has an $x^2$ term, so it is nonlinear (quadratic).

Step3: Identify linearity of Function 3

Check the rate of change: $\frac{2-1}{-2-(-4)}=\frac{1}{2}$, $\frac{3-2}{0-(-2)}=\frac{1}{2}$, $\frac{4-3}{2-0}=\frac{1}{2}$. Constant slope means it is linear.

Step4: Evaluate each option

• A: False, Function 3 is also linear.
• B: False, Functions 1 and 3 are linear.
• C: True, Functions 1 and 3 are linear; Function 2 is not.
• D: False, only Function 2 is nonlinear.

Answer:

C. Function 1 and Function 3 are the only linear functions.