Question

cubic & cube root functions unit online practice
complete this assessment to review what youve learned. it will not count toward your g
how does the graph of $f(x) = \sqrt3{x}$ change when $f(x)$ is replaced by $-7f(x)$? (1 point)
\bigcirc the graph is reflected across the $y$-axis and has been compressed vertically.
\bigcirc the graph is reflected across the $y$-axis and has been compressed horizontally.
\bigcirc the graph is reflected across the $x$-axis and has been stretched horizontally.
\bigcirc the graph is reflected across the $x$-axis and has been stretched vertically.
check answer remaining attempts : 3

Explanation:

Step1: Analyze reflection

For a function \( y = f(x) \), replacing \( f(x) \) with \( -f(x) \) reflects the graph across the \( x \)-axis. Here we have \( -7f(x) \), so the negative sign means reflection across the \( x \)-axis.

Step2: Analyze vertical stretch/compression

For a function \( y = f(x) \), replacing \( f(x) \) with \( a f(x) \) (where \( |a|>1 \)) vertically stretches the graph, and if \( 0<|a|<1 \) it compresses. Here \( a = 7 \) (since \( | - 7|=7>1 \)), so it's a vertical stretch.

Answer:

The graph is reflected across the \( x \)-axis and has been stretched vertically. (The option: The graph is reflected across the \( x \)-axis and has been stretched vertically)