What transformation produce the graph of g(x)= -|8x| from the graph of the parent function f(x)=|x|?
a. horizontal stretch by a factor of 8
b. horizontal compression by a factor of 8
c. vertical stretch by a factor of 8
d. vertical compression by a factor of 8
e. reflection over the y-axis
f. reflection over the x-axis
i have no idea what to do.. please help
To determine the transformation that produces the graph of g(x) = -|8x| from the graph of the parent function f(x) = |x|, we need to analyze the changes made to the original function.
1. Vertical Stretch/Compression: If the graph of f(x) = |x| is vertically stretched or compressed, the absolute value will remain the same, but the vertical size of the graph will change. However, in the given function g(x) = -|8x|, there is no vertical stretch or compression by a factor of 8, as the absolute value is unchanged.
2. Horizontal Stretch/Compression: If the graph of f(x) = |x| is horizontally stretched or compressed, the absolute value will change, affecting the steepness of the graph. In the given function g(x) = -|8x|, the absolute value is modified by multiplying the input, x, by 8, resulting in the graph being horizontally compressed by a factor of 8.
3. Reflection over the y-axis: If the graph of f(x) = |x| is reflected over the y-axis, the positive and negative values will switch. In the given function g(x) = -|8x|, the negative sign in front of the absolute value causes the reflection over the y-axis.
4. Reflection over the x-axis: If the graph of f(x) = |x| is reflected over the x-axis, the positive and negative values will switch, and the graph will "flip" upside down. However, in the given function g(x) = -|8x|, there is no reflection over the x-axis.
Based on the analysis, the correct transformation that produces the graph of g(x) = -|8x| from the graph of f(x) = |x| is:
e. reflection over the y-axis.
To determine the transformation that produces the graph of g(x) = -|8x| from the graph of the parent function f(x) = |x|, we need to understand the effects of each possible transformation.
1. Horizontal stretch by a factor of 8: This transformation would cause the graph to become wider. However, in the given function g(x) = -|8x|, there is no horizontal stretching.
2. Horizontal compression by a factor of 8: This transformation would cause the graph to become narrower. However, in the given function g(x) = -|8x|, there is no horizontal compression.
3. Vertical stretch by a factor of 8: This transformation would cause the graph to become taller. However, in the given function g(x) = -|8x|, the vertical stretch is not a factor.
4. Vertical compression by a factor of 8: This transformation would cause the graph to become shorter. However, in the given function g(x) = -|8x|, there is no vertical compression.
5. Reflection over the y-axis: This transformation would cause the graph to be mirrored along the y-axis. In the given function g(x) = -|8x|, there is indeed a reflection over the y-axis, as the negative sign before the absolute value causes the graph to be reflected.
6. Reflection over the x-axis: This transformation would cause the graph to be mirrored along the x-axis. However, in the given function g(x) = -|8x|, there is no reflection over the x-axis.
Based on the explanations above, the correct transformation that produces the graph of g(x) = -|8x| from the graph of the parent function f(x) = |x| is the reflection over the y-axis. Therefore, the answer is option e. reflection over the y-axis.
You need to look in your notes and recall what each transformation (that is... what a compresssion, reflection, etc) do to the original graph.
In younger grades you recall that y=x is obtained from y=(x+2) by a horizontal translation (slide) of each of the points... 2 units to the RIGHT.
Your notes describe what each transformation does.