Question

The graph below shows the solution for the following system.

{f(x)=2x−3
g(x)=2^x−4
Linear function passing through (0, negative 3), (1.5, 0) & about (2.7, 2.3).
Exponential function passing through (negative 3, negative 4), (0, negative 3), (2,0) & about (2.7, 2.3).


Which statements are true?

Select all that apply.

x=0 is a solution to the system.

(1.5,0) and (2,0) are solutions to the system because the graphs of f(x) and g(x) cross the x-axis at those points.

When x≈2.7, the graphs of f(x) and g(x) intersect because they are equal to each other at that value.

f(x)=g(x) when x=0.

Answer 1

f(x)=g(x) when x=0.

x=0 is a solution to the system.

When x≈2.7, the graphs of f(x) and g(x)intersect because they are equal to each other at that value.

Answer 2

TRUE:

When x≈2.7, the graphs of f(x) and g(x) intersect

f(x)=g(x) when x=0

Explanation:

The graphs of two function y=f(x) and y=g(x) are shown in attached diagram.

These two graphs intersect at two points (0,-3) and about (2.7,2.3). This means that

f(0)=g(0)=-3

and

f(2.7)=g(2.7)=2.3

So, x=0, y=-3 is the solution to the system (the solution to the system is ordered pair (x,y), not only x)

Points (1.5,0) and (2,0) are not solutions, because they are not points of graphs intersection.

When x≈2.7, the graphs of f(x) and g(x) intersect (TRUE)

f(x)=g(x) when x=0 (TRUE)