The function g(x) after using the transformation rules given is; g(x) = -|8x| + 5
We can deduce that the sentence "compress f(x) by a factor of 1/2" means that horizontal distances on the graph of f(x) are to be reduced to 1/2 their value to obtain the graph of g(x). This means the graph has been reduced by a scale factor of 1/2.
If k is the horizontal scale factor, then the horizontal scaling makes g(x) to be expressed as;
g(x) = f(x/k)
Reflection across the x-axis changes the sign of function values, so our compressed, reflected function is;
g(x) = -f(x/(1/2)) = -f(2x)
g(x) = -(|4(2x)| -5)
g(x) = -|8x| +5
Complete question is;
Let g(x) be the indicated transformation of f(x) = |4x| − 5. Compress the graph of f(x) = |4x| − 5 horizontally by a factor of 1/2 and reflect it across the x-axis. Identify the rule and graph of g(x).
Read more about Graph Transformation at; https://brainly.com/question/4289712
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