Question

cubic & cube root functions unit online practice
complete this assessment to review what you’ve learned. it will not count toward
how does the graph of f(x) = sqrt3{x} change when f(x) is replaced by 7f(x)? (1 point)
the graph moves up 7 units.
the graph moves down 7 units.
the graph moves to the right 7 units.
the graph does not shift left or right.
check answer remaining attempts 3

Explanation:

Step1: Recall function transformation rules

For a function \( y = f(x) \), when we have \( y = a f(x) \) (vertical scaling), horizontal shifts are caused by changes to the input \( x \) (like \( f(x - h) \) for horizontal shift by \( h \) units), and vertical shifts by changes to the output (like \( f(x)+k \) for vertical shift by \( k \) units). Here, we have \( 7f(x) \), which is a vertical scaling (stretching by a factor of 7), not a horizontal shift (which would involve changing \( x \) inside the function, e.g., \( f(x - 7) \)) or vertical shift (which would be \( f(x)+7 \) or \( f(x)-7 \)).

Step2: Analyze each option

• "The graph moves up 7 units": This would be \( f(x)+7 \), not \( 7f(x) \), so incorrect.
• "The graph moves down 7 units": This would be \( f(x)-7 \), not \( 7f(x) \), so incorrect.
• "The graph moves to the right 7 units": This would be \( f(x - 7) \), not \( 7f(x) \), so incorrect.
• "The graph does not shift left or right": Since \( 7f(x) \) is a vertical transformation (scaling) and not a horizontal transformation (which affects the \( x \)-input), there is no horizontal shift (left or right). So this is correct.

Answer:

The graph does not shift left or right.