Question

8 multiple choice 10 points which best represents the transformation from the parent function f(x) = |x| to the new function g(x) = \frac{1}{3}|x| - 4 \bigcirc g(x) is shifted down 4 units and is 1/3 as steep \bigcirc g(x) is shifted up 4 units and is 1/3 as steep \bigcirc g(x) is shifted down 4 units and is 3 times as steep \bigcirc g(x) is shifted up 4 units and is 3 times as steep

Explanation:

Step1: Analyze vertical shift

For a function \(y = f(x)+k\), if \(k>0\), it shifts up; if \(k < 0\), it shifts down. In \(g(x)=\frac{1}{3}x - 4\), comparing with \(f(x)=x\) (which can be written as \(f(x)=1\times x+0\)), the constant term is \(- 4\), so it is a shift down by 4 units.

Step2: Analyze slope (steepness)

The slope of \(f(x)=x\) is \(m = 1\), and the slope of \(g(x)=\frac{1}{3}x-4\) is \(m=\frac{1}{3}\). Since \(\frac{1}{3}<1\), the line is less steep, specifically \(\frac{1}{3}\) as steep as the parent function.

Answer:

\(g(x)\) is shifted down 4 units and is \(1/3\) as steep