Asked by bob

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Five labeled curves with bidirectional arrows are plotted on a coordinate plane.
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The values on the x-axis range from negative 4 to 6 in increments of 1. The values on the y-axis range from negative 4 to 4 in increments of 1. A solid curve plotted in quadrants 1 and 2 is labeled f left parenthesis x right parenthesis equals 2 superscript x. The solid curve passes through left parenthesis negative 4 comma 0 right parenthesis, left parenthesis 0 comma 1 right parenthesis, left parenthesis 1 comma 2 right parenthesis, and left parenthesis 2 comma 4 right parenthesis. A dotted curve labeled Option 1 is plotted in quadrants 3 and 4. The dotted curve passes through left parenthesis negative 4 comma negative 0.1 right parenthesis, left parenthesis 0 comma negative 1 right parenthesis, left parenthesis 1 comma negative 2 right parenthesis, and left parenthesis 2 comma negative 4 right parenthesis. A dashed curve labeled Option 2 is plotted in quadrants 3 and 4. The dashed curve passes through left parenthesis 6 comma 0 right parenthesis, left parenthesis 0 comma negative 1 right parenthesis, left parenthesis negative 1 comma negative 2 right parenthesis, and left parenthesis negative 2 comma negative 4 right parenthesis. A dot-dashed curve labeled Option 3 is plotted in quadrants 1 and 2. It passes through left parenthesis 6 comma 0.1 right parenthesis, left parenthesis 0 comma 1 right parenthesis, left parenthesis negative 1 comma 2 right parenthesis, and left parenthesis negative 2 comma 4 right parenthesis. A dot-dot-dashed curve labeled Option 4 is plotted in quadrant 1. This solid curve passes through left parenthesis 6 comma 0.2 right parenthesis, left parenthesis 4 comma 1 right parenthesis, left parenthesis 3 comma 2 right parenthesis, and left parenthesis 2 comma 4 right parenthesis. All values are approximate.

Describe the transformation of the graph of f(x)=2x
to the graph labeled Option 3.

(1 point)

Option 3 is the graph of −f(x)
.

Option 3 is the graph of f(−x)
.

Option 3 is the graph of f(x−1)
.

Option 3 is the graph of −f(−x)
.

All Answers 1

Answered by GPT-5 mini AI
Option 3 is the graph of f(−x).

Reason: Option 3 has points (0,1), (−1,2), (−2,4), which satisfy Option3(x)=f(−x) because Option3(−1)=f(1)=2, Option3(−2)=f(2)=4, etc. This is a reflection of f(x)=2^x across the y-axis.