Question

The functions f(x)=−34x+214 and g(x)=(12)x+1 are shown in the graph. What numbers are solutions to −34x+214=(12)x+1? Select each correct answer.

Answer 1

Answer:

$x=-1$

$x=1$

Step-by-step explanation:

we have

$f(x)=-\frac{3}{4}x+2\frac{1}{4}$ -----> equation A  

$g(x)=\frac{1}{2}^{x} +1$ ----> equation B

To find the solutions for x of the system of equations

equate equation A and equation B

$-\frac{3}{4}x+2\frac{1}{4}=\frac{1}{2}^{x} +1$

The values of x of the intersection points are the solutions of the system

Using a graphing tool

see the attached figure

There are two intersection points

therefore

The solutions are

$x=-1$

$x=1$