Question

The question is: "Without actually graphing, describe how the graph of y = ( -2^(x+17) ) - 4.3 is related to the graph of y = 2^x"

Answer 1

The function has been flipped due to the negative in front.

The function has been shifted 17 units to the left.

The function has been shifted 4.3 units down.

Explanation:

When functions are transformed there are a few simple rules:

• Adding/subtracting inside the parenthesis to the input shifts the function left(+) and right(-).
• Adding/subtracting outside the parenthesis to the output shifts the function up(+) and down(-).
• Multiplying the function by a number less than 1 compresses it towards the x-axis.
• Multiplying the function by a number greater than 1 stretches it away from the x-axis.
• Multiplying by a negative flips the graph.

The graph of
`(-2^(x+17)) -4.3` compares to
`2^x` in the following ways:

The function has been flipped due to the negative in front.

The function has been shifted 17 units to the left.

The function has been shifted 4.3 units down.