Starting with the graph of f(x) = 5^{x}, write the equation of the graph that results from (a) shifting f(x) 1 units downward. y =? (b) shifting f(x) 1 units to the left. y =? (c) reflecting f(x) about the x-axis. y =?

1 down, means minus 1 from whole equation
moving 1 to left means add 1 to every x
reflecting across x axis means multiply every x by -1

a. [tex]y=5^x+1[/tex]
b. [tex]y=5^{x+1}[/tex]
c. [tex]y=5^{-x}[/tex]

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psm22415 psm22415 · Answer 2 · 2021-12-01T06:49:01+01:00

The equation after shifting 1 unit downward, [tex]y = 5^{x} + 1[/tex]

The equation after shifting 1 unit of the left, [tex]y = 5^{-x}[/tex]

Given that,

Graph of f(x) = [tex]5^{x}[/tex]

We have to find,

The equation of the graph that results from,

Shifting f(x) 1 units downward y is,

Shifting f(x) 1 units to the left. y is,

Reflecting f(x) about the x-axis. y = is.

According to the question,

The function [tex]f(x) = 5^{x}[/tex]

When Shifting f(x) 1 units downward y is,

The equation after shifting 1 unit downward,

[tex]y = 5^{x} + 1[/tex].

Shifting f(x) 1 units to the left. y is,

The equation after shifting 1 unit of the left,

[tex]y = 5^{x+1}[/tex]

Reflecting f(x) about the x-axis. y is,

The equation after shifting 1 unit of the left,

[tex]y = 5^{-x}[/tex]

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