How can you use transformations to graph this function? y= 3•7^-x+2 explain your steps.

The parent function for this function is 



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

Let y=g(x)

So, 



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

Letter a i would say

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

answer: the function g(x) has the greatest slope.