Chapter 7.6, Problem 43PPE

a.

To determine

To calculate:graphgiven functions on the same axes.

Answer to Problem 43PPE

  

Explanation of Solution

Given information: $y=2^x,y=4^x$ and $y={0.25}^x$

Calculation:

Let’s plot the given functions,

  

b.

To determine

To calculate:what point is on all three graphs.

Answer to Problem 43PPE

  $(0,1)$

Explanation of Solution

Given information: $y=2^x,y=4^x$ and $y={0.25}^x$

Calculation:

Let’s plot the given functions,

  

From the graph it is clear that point $(0,1)$ is on all the three graphs

c.

To determine

To calculate:does the graph intersects $x$ axis. Explain.

Answer to Problem 43PPE

No

Explanation of Solution

Given information: $y=2^x,y=4^x$ and $y={0.25}^x$

Calculation:

Graph of an exponential function never intersects an $x$ axis, because exponential functions can not give negative values, they only give positive values.

d.

To determine

To calculate:how does the graph of $y=b^x$ changes with the $b$ .

Answer to Problem 43PPE

For $b<1$ , graph reaches to infinite for negative $x$ value. For $b>1$ , graph reaches to infinite for positive $x$ value. As $b$ increases, graph reaches infinite early

Explanation of Solution

Given information: $y=2^x,y=4^x$ and $y={0.25}^x$

Calculation:

For $b<1$ , graph reaches to infinite for negative $x$ value. For $b>1$ , graph reaches to infinite for positive $x$ value. As $b$ increases, graph reaches infinite early