Chapter 8.6, Problem 36E

To determine

To Match: The graph with its equation.

Answer to Problem 36E

Graph A matches with $y=2x-4$

Graph D matches with this equation y=2x²-4

Graph B matches with $y=2{(\frac{3}{4})}^x+1$ .

Graph C matches with the function $y=2{(4)}^x+1$ .

Explanation of Solution

Given information: It is given with graph and equations.

Calculation:

The linear equation $y=2x-4$ gives a graph of line.

Graph “A” matches with $y=2x-4$

The quadratic equation $y=2x^2-4$ gives a graph as Parabola.

Graph “D” matches with this equation $y=2x^2-4$ .

Now, let’s match the exponential equations.

The $y=2{(\frac{3}{4})}^x+1$ has the base for exponent as fraction which is less than 1 but more than 0. So, graph this exponential function would be decreasing.

So, Graph B matches with $y=2{(\frac{3}{4})}^x+1$ .

The $y=2{(4)}^x+1$ it is exponential function which has base to x as 4. So, graph this function is increasing. Graph C matches with the function $y=2{(4)}^x+1$ .