Question

use the table and graph to compare the two functions.

x	f(x)
-1	6
0	4
1	2
2	0

(graph of g(x) is a line on a coordinate grid)

which statements about f(x) and g(x) are true? select all that apply.

□ a) the x - intercept of g(x) is greater than the x - intercept of f(x)

□ b) the y - intercept of g(x) is greater than the y - intercept of f(x)

□ c) f(x) decreases while g(x) increases

□ d) the slope of g(x) is greater than the slope of f(x)

Explanation:

Step1: Find slope of $f(x)$

Slope formula: $m=\frac{f(x_2)-f(x_1)}{x_2-x_1}$
Take $(x_1,y_1)=(0,4),(x_2,y_2)=(1,2)$:
$m_f=\frac{2-4}{1-0}=-2$

Step2: Find intercepts of $f(x)$

Y-intercept: when $x=0$, $f(0)=4$
X-intercept: when $f(x)=0$, $x=2$

Step3: Find slope of $g(x)$

Take $(x_1,y_1)=(0,-2),(x_2,y_2)=(2,-1)$:
$m_g=\frac{-1-(-2)}{2-0}=\frac{1}{2}$

Step4: Find intercepts of $g(x)$

Y-intercept: when $x=0$, $g(0)=-2$
X-intercept: when $g(x)=0$, $x=4$

Step5: Evaluate each option

A) $4>2$ → True
B) $-2>4$ → False
C) $f(x)$ slope $<0$ (decreases), $g(x)$ slope $>0$ (increases) → True
D) $\frac{1}{2}>-2$ → True

Answer:

A) The x-intercept of $g(x)$ is greater than the x-intercept of $f(x)$
C) $f(x)$ decreases while $g(x)$ increases
D) The slope of $g(x)$ is greater than the slope of $f(x)$