Question

1. the function ( f(x) ) is represented by the graph. the function ( g ) is defined by ( g(x) = -2x + 3 )

determine which statements are true. select all that apply.

a) ( f(1) < g(1) )
b) ( f(-2) < g(-2) )
c) ( f(4) > g(4) )
d) ( f(2) > g(2) )
2 points
(f.if.c.9)

Explanation:

Step1: Analyze \( f(1) \) and \( g(1) \)

From the graph, at \( x = 1 \), \( f(1)=9 \). For \( g(x)=-2x + 3 \), substitute \( x = 1 \): \( g(1)=-2(1)+3 = 1 \). So \( f(1)=9>1 = g(1) \), so statement a is false.

Step2: Analyze \( f(-2) \) and \( g(-2) \)

From the graph, at \( x=-2 \), \( f(-2)=0 \) (since it crosses the x - axis at \( x=-2 \)). For \( g(x) \), substitute \( x=-2 \): \( g(-2)=-2(-2)+3=4 + 3=7 \). So \( f(-2)=0<7 = g(-2) \), statement b is true.

Step3: Analyze \( f(4) \) and \( g(4) \)

From the graph, at \( x = 4 \), \( f(4)=0 \) (crosses x - axis at \( x = 4 \)). For \( g(x) \), substitute \( x = 4 \): \( g(4)=-2(4)+3=-8 + 3=-5 \). So \( f(4)=0>-5=g(4) \), statement c is true.

Step4: Analyze \( f(2) \) and \( g(2) \)

From the graph, at \( x = 2 \), \( f(2)=9 \) (since the vertex is around \( x = 1 \), and it's symmetric, \( f(2) \) is close to the maximum value). For \( g(x) \), substitute \( x = 2 \): \( g(2)=-2(2)+3=-4 + 3=-1 \). So \( f(2)=9>-1=g(2) \), statement d is true.

Answer:

b) \( f(-2) < g(-2) \), c) \( f(4) > g(4) \), d) \( f(2) > g(2) \)