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. \(y=5^x+1\)
b. \(y=5^{x+1}\)
c. \(y=5^{-x}\)

Answer Link

psm22415 psm22415 · Answer 2 · 2021-12-01T00:49:01-05:00

The equation after shifting 1 unit downward, \(y = 5^{x} + 1\)

The equation after shifting 1 unit of the left, \(y = 5^{-x}\)

Given that,

Graph of f(x) = \(5^{x}\)

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 \(f(x) = 5^{x}\)

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

The equation after shifting 1 unit downward,

\(y = 5^{x} + 1\).

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

The equation after shifting 1 unit of the left,

\(y = 5^{x+1}\)

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

The equation after shifting 1 unit of the left,

\(y = 5^{-x}\)

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