Question

The functions f(x)=−34x+214 and g(x)= (12)x+1 is shown in the graph.

What are the solutions to −34x+214= (12)x+1?

Select each correct answer.




−1

0

1

2

3
An exponential curve and a line graphed on a coordinate plane. The horizontal x-axis ranges from negative 4 to 4 in increments of 1. The vertical y-axis ranges from negative 4 to 4 in increments of 1. The curve begins in the second quadrant. The curve decreases through begin ordered pair 0 comma 2 end ordered pair. The curve passes through begin ordered pair negative 1 comma 3 end ordered pair and begin ordered pair 1 comma 1.5 end ordered pair and exits the first quadrant. The line passes through begin ordered pair 0 comma 2.25 end ordered pair and begin ordered pair 3 comma 0 end ordered pair. The curve and the line intersects at begin ordered pair negative 1 comma 3 end ordered pair and begin ordered pair 1 comma 1.5 end ordered pair.

Answer 1

x = -1 and x = +1

Explanation:

The solution to f(x) = g(x) is found where the graphs intersect.

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Your problem statement tells you the solution:

"The curve and the line intersects at begin ordered pair negative 1 comma 3 end ordered pair and begin ordered pair 1 comma 1.5 end ordered pair."

We interpret this statement to mean the points of intersection are ...

(-1, 3) and (1, 1.5)

The x-values that make f(x) = g(x) are x=-1 and x=1.