Question

Use the graph that shows the solution to f(x)=g(x) . (Images below)

f(x)=7/3x−3

g(x)=2^x−4


What is the solution to f(x)=g(x) ?

Select each correct answer.




−1/2

0

2

3

Answer 1

Here's my step-by-step explanation:

Let's get two facts straight: f(x) is a linear function. It's a line. g(x) is an exponential function. It's a curve.

Method 1: Elimination using f(x)

For f(x), the y-intercept (where on the y-axis it coincides with) in {f(x) = 7/3x - 3} is -3. And the only graph that has that is Graph 2.

Alright, so the first obvious solution, according to that graph, is (0, -3). And since we're speaking in terms of x (thus f(x) and g(x)), we pick the x-value from that coordinate and get 0.

The second solution is not as obvious; it's supposed to be (3,4) but the graph is kinda off. I attached a Desmos graph so you can see what I'm talking about a little more clearly.

Anyway, since we're speaking in terms of x we pick the x-value from that coordinate and get 3. Nice, we've got the solutions 0 and 3.

Hope this helps, let me know if I made a mistake.