Question

Which equation represents the transformation of f(x)=|x| when effected by a reflection over the x-axis, a vertical shrink by 14 and a vertical shift up 6 units? Responses g(x)=−4|x|+6 g open parentheses x close parentheses equals negative 4 open vertical bar x close vertical bar plus 6 g(x)=−4|x+6| g open parentheses x close parentheses equals negative 4 open vertical bar x plus 6 close vertical bar g(x)=−14|x|+6 g open parentheses x close parentheses equals negative 1 fourth open vertical bar x close vertical bar plus 6 g(x)=−14|x+6|

Answer 1

The transformation of the function f(x) = |x| after being reflected over the x-axis, vertically shrunk by 14, and shifted up by 6 units is represented by the equation g(x) = -1/14|x| + 6.

Step-by-step explanation:

The original function is f(x) = |x|. To find the transformation of this function after a reflection over the x-axis, a vertical shrink by 14, and a vertical shift up by 6 units, we must apply these transformations step by step.

First, a reflection over the x-axis will change the sign of the function, so f(x) becomes -f(x) = -|x|.

Next, a vertical shrink by a factor of 14 means we multiply the function by 1/14, so our function now becomes (-1/14)|x|. Finally, a vertical shift up by 6 units adds 6 to our function, resulting in g(x) = (-1/14)|x| + 6.

Therefore, the equation that represents the transformation is g(x) = -1/14|x| + 6.