Question

algebra 2a semester online practice
complete this assessment to review what you’ve learned. it will not count toward your grad
how does the graph of $f(x) = \sqrt3{x}$ change when $f(x)$ is replaced by $f(-0.25x)$? (1 point)
\bigcirc the graph is reflected over the x-axis and compresses horizontally.
\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 y-axis and stretches vertically.
check answer remaining attempts: 3

Explanation:

Step1: Analyze reflection

For a function \( y = f(x) \), replacing \( x \) with \( -x \) reflects the graph over the \( y \)-axis. Here, we have \( f(-0.25x) \), so the \( x \)-input has a negative sign, indicating a reflection over the \( y \)-axis.

Step2: Analyze horizontal stretch/compression

The general rule for horizontal transformations: if we have \( y = f(kx) \), when \( |k| < 1 \), the graph stretches horizontally; when \( |k| > 1 \), it compresses horizontally. Here, \( k=-0.25 \), and \( | - 0.25|=0.25<1 \), so the graph stretches horizontally.

Answer:

The graph is reflected over the y - axis and stretches horizontally (corresponding to the option: The graph is reflected over the y - axis and stretches horizontally)