The graph of y=$\sqrt [ 3 ] { x }$ is shifted 3.5 units to the left. This graph is then vertically stretched by a factor of 5.1. Finally, the graph is reflected across the x -axis.
A) $y = - 5.1 \sqrt [ 3 ] { x - 3.5 }$
B) $y = 5.1 \sqrt [ 3 ] { x + 3.5 }$
C) $y = - 5.1 \sqrt [ 3 ] { x + 3.5 }$
D) $y = - 3.5 \sqrt [ 3 ] { x + 5.1 }$

Question

The graph of  y=$\sqrt [ 3 ] { x }$  is shifted  3.5  units to the left. This graph is then vertically stretched by a factor of 5.1. Finally, the graph is reflected across the  x -axis.
A) $y = - 5.1 \sqrt [ 3 ] { x - 3.5 }$
B) $y = 5.1 \sqrt [ 3 ] { x + 3.5 }$
C) $y = - 5.1 \sqrt [ 3 ] { x + 3.5 }$
D) $y = - 3.5 \sqrt [ 3 ] { x + 5.1 }$

Quizplus · Accepted Answer

Shifting the graph 3.5 units to the left means replacing $x$ with $x + 3.5$. A vertical stretch by a factor of 5.1 multiplies the function by 5.1. Reflecting across the x-axis multiplies the function by -1. Therefore, the correct transformation is $y = -5.1\sqrt[3]{x + 3.5}$.

The Graph of Y= x3\sqrt [ 3 ] { x }3x​

The Graph of Y= $\sqrt [ 3 ] { x }$