Question

How can you use transformations to graph this function?

Answer 1

Answer:

Sketch the graph of y=7^x

Reflect the graph across the y-axis to show the function y=7^-x

Stretch the graph vertically by a factor of 3 to show the function y= 3*7^-x

Shift the graph up 2 units to show the function y=3*7^-x+2

Step-by-step explanation:

Answer 2

The parent function for this function is 

$f(x)= 7^{x}$

We have to explain how the given function can be obtained from the parent function.

Let y=g(x)

So, 

$g(x)=3*7^{-x} +2$

Notice that x in the exponent is multiplied by -1. Multiplying x by -1 implies the reflection of the graph across y-axis.

The function value is multiplied by 3. This suggest a vertical expansion by a factor of 3.

2 is being added to the function value, this implies a vertical shift upwards by 2 units.

So, we can write:

y = g(x) = 3f(-x) + 2

Thus following translations are applied:

a) Reflection across y-axis
b) Vertical stretch by a factor of 3
c) Upward shift by 2 units