Question

The points on the graph represent both an exponential function and a linear function.

Answer 1

By looking at the graphs we can infer the equation that represents both functions. If we plot the equations in a graphing tool, we can easily find your points.

Please, see the attached image

Linear

f(x)  = (-3/2)*x + 3

x = -3 ---------> y = 15/2 = 7.5

x = -2 ---------> y = 6

x = -1 ---------> y = 4.5

x = 0 ---------> y = 3

x = 1 ---------> y = 1.5

x = 2 ---------> y = 0

x = 3 ---------> y = -1.5

Exponential

g(x)  = (1/2)^x

x = -3 ---------> y = 8

x = -2 ---------> y = 4

x = -1 ---------> y = 2

x = 0 ---------> y = 1

x = 1 ---------> y = 0.5

x = 2 ---------> y = 0.25

x = 3 ---------> y = 0.125

(1/2)^x =  (-3/2)*x + 3

If we solve this equation, we get two values

x = -2.868 and

x = 1.81

Answer 2

Answer:

Step-by-step explanation:

From the graph attached we will find the linear as well as exponential functions first.

Afterwards we will plug in the values of x to get the value of the function given.

For Linear function

It should be in the form of y = mx + c

We find c = 3

and two points passing through the line are (0, 3) and (2, 0)

so slope of the line should be $m=\frac{y-y'}{x-x'}= \frac{3-0}{0-2}=-\frac{3}{2}$

Now we can say the linear function becomes $f(x)=-\frac{3}{2}x+3$

For x = -3, $f(3)=(-\frac{3}{2})(3)+3=(-\frac{9}{2})+3=(-\frac{3}{2})$

For x = -2 $f(-2)=(-\frac{3}{2})(-2)+3=3+3=6$

For x = -1 $f(-1)=(-\frac{3}{2})(-1)+3=\frac{3}{2}+3=\frac{9}{2}$

For x = 0 $f(0)=3$

For x = 1 $f(1)=-\frac{9}{2}$

For x = 2 f(2) = -6

For x = 3 $f(3)=\frac{3}{2}$

Now for Exponential function

function will be in the form of $y=a^{x}$

Since point (-1, 2) is passing through the exponential function

So $2=(a)^{-1}=\frac{1}{a}$

⇒$a=\frac{1}{2}$

Therefore exponential function is $g(x)=(\frac{1}{2})^{x}$

Now from the given graph

g(-3) = 8

g(-2) = 6

g(-1) = 2

g(0) = 1

$g(1)=\frac{1}{2}$

$g(2)=(\frac{1}{2})^{2}=\frac{1}{4}=0.75$

$g(3)=(\frac{1}{2})^{3}=\frac{1}{8}=0.125$

Now we will try to get the common values of x by analyzing the graphs of two functions.

we get the solutions for x as (-2.87) and (1.81)