Question

cubic & cube root functions unit online practice
complete this assessment to review what you’ve learned. it will not count toward yo
how does the graph of $f(x) = \sqrt3{x}$ change when $f(x)$ is replaced by $f(-0.7x)$? (1 po
\bigcirc the graph is reflected over the $y$-axis and stretches horizontally.
\bigcirc the graph is reflected over the $x$-axis and compresses vertically.
\bigcirc the graph is reflected over the $x$-axis and compresses horizontally.
\bigcirc the graph is reflected over the $y$-axis and stretches vertically.

Explanation:

Step1: Analyze reflection

For a function \( y = f(x) \), replacing \( x \) with \( -x \) reflects the graph over the \( y \)-axis. Here, we have \( f(-0.7x) \), so the \( x \) is replaced with \( -0.7x \), which includes a sign change (\( -x \) component), so there is a reflection over the \( y \)-axis.

Step2: Analyze horizontal stretch/compression

The general rule for horizontal transformations: if we have \( y = f(kx) \), when \( |k|>1 \), it's a horizontal compression; when \( 0<|k|<1 \), it's a horizontal stretch. Here, \( k = -0.7 \), and \( | - 0.7|=0.7<1 \), so it's a horizontal stretch (since \( |k| < 1 \), the graph stretches horizontally).

Answer:

A. The graph is reflected over the \( y \)-axis and stretches horizontally.