Chapter 6.3, Problem 26E

To determine

To find:Function of each graph.

Answer to Problem 26E

Each graph is matched with its function.

Explanation of Solution

Given information :

Linear & exponential function.

Concept used:

Use patterns between consecutive data pairs to determine type of function.

Linear function: - The difference of consecutive y-values is constant.

Consecutive ‘y’ values have a common ratio and they do not change by a constant amount.

Exponential function: - Consecutive y-values have a common ratio. In each case, the differences of consecutive x-values need to be constant.

Consecutive y values change by a constant ratio.

  

  

As we can see from the above given graph

Graph (a)

  $x-$ intercept is positive & $y-$ intercept is negative. Slope is positive & function is linear.

Function is $y=2x-4$

Graph (b)

  $x-$ intercept is in infinity& $y-$ intercept is positive. Slope is not constant& function is exponential. As $x-$ moves towards infinity $y-$ move towards 1.

Function is $y=2{(\frac{3}{4})}^x+1$

Graph (c)

  $x-$ intercept is in infinity & $y-$ intercept is positive. Slope is not constant& function is exponential.As $x-$ moves towards negative infinity $y-$ move towards 1.

Function is $y=2{(4)}^x+1$

Graph (d)

  $x-$ intercept is positive & $y-$ intercept is positive. Slope is negative& function is linear.

Function is $y=-\frac{1}{2}x+1$

Hence,

Each graph is matched with its function.