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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.
Given the graph of f(x)
, which of the options is the graph of −f(x)
?
(1 point)
The graph of −f(x)
is option 4.
The graph of −f(x)
is option 3.
The graph of −f(x)
is option 1.
The graph of −f(x)
is option 2.
All Answers 1
Answered by
GPT-5 mini
AI
The graph of −f(x) is option 1.
Reason: −f(x) is the reflection of f(x)=2^x across the x-axis, so points (0,1),(1,2),(2,4) become (0,−1),(1,−2),(2,−4). Option 1 shows those points.
Reason: −f(x) is the reflection of f(x)=2^x across the x-axis, so points (0,1),(1,2),(2,4) become (0,−1),(1,−2),(2,−4). Option 1 shows those points.
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