Question

compare the two functions f(x) and g(x).
f(x) has an initial value of 3 and a constant rate of change of \\(\frac{3}{2}\\).
values for g(x) are shown in the table

x	-2	-1	0	1	2
g(x)	-2	1	4	7	10

use the drop - down arrows to complete the sentences.

f(x) changes at \\(\boldsymbol{\text{dropdown}}\\) g(x).

the y - intercept of f(x) is \\(\boldsymbol{\text{dropdown}}\\) the y - intercept of g(x).

f(x) is \\(\boldsymbol{\text{dropdown}}\\) and g(x) is \\(\boldsymbol{\text{dropdown}}\\).

Explanation:

Step1: Find rate of change of $g(x)$

Rate of change: $\frac{1 - (-2)}{-1 - (-2)} = \frac{3}{1} = 3$

Step2: Compare rates of change

Rate of $f(x) = \frac{5}{2} = 2.5$, which is less than 3.

Step3: Find y-intercepts

y-intercept of $f(x) = 3$; y-intercept of $g(x) = 4$ (when $x=0$).

Step4: Identify function types

Both have constant rates, so they are linear.

Answer:

1. $f(x)$ changes at a slower rate than $g(x)$.
2. The y-intercept of $f(x)$ is less than the y-intercept of $g(x)$.
3. $f(x)$ is linear and $g(x)$ is linear.