Question

Use the graph that shows the solution to F(x) = G(x)

Answer 1

Answer: B. 0 and D. 3

Step-by-step explanation:

Here the given function is,

$f(x) = \frac{7}{3}x-3$

$g(x) = 2^x-4$

For finding the solution of this system of equation,

First we will plot the function on the graph,

Graph of function f(x),

x-intercept and y-intercept are (1.286,0) and (0,-3) respectively,

Also, it is a straight line,

Hence, we can plot this line on the graph,

Graph of function g(x),

Function g(x) is an exponential function having x-intercept and y -intercept, (2,0) and (0,-3) respectively.

Also, the end behavior is,

As $x\rightarrow \infty$ , $f(x)\rightarrow \infty$

As  $x\rightarrow -\infty$ , $f(x)\rightarrow -4$

Hence, we can plot the graph of g(x),

By plotting the graph,

We found that the intersection of the function f(x) and g(x) are (0,-3) and (3,4).

Hence, the solution of the system is the x-coordinates of the intersection points that are 0 or 3.

⇒ Option B and C is the correct options.

 

Answer 2

Answer:

Option (b) and (d)  is correct.

The solution where f (x) = g(x)  is when x = 0 and x = 3

Step-by-step explanation:

Given : functions $F(x) = \frac{7}{3}x-3$ and $G(x) =2^x-4$

We have to find the solution where f (x) = g(x)

Consider the given function  $F(x) = \frac{7}{3}x-3$ and $G(x) =2^x-4$

The solution where f (x) = g(x)  is the point where both graph intersect at y- axis.

Then it is seen clearly from graph of both the functions intersect at point (0, -3) and (3,4)

When x = 0 both f(0) and g(0) = -3

When x = 3 both f(3) and g(3) = 4

Thus, the  solution where f (x) = g(x)  is when x= 0 and x= 3

Thus, Option (b) and (d) is correct.