Question

section 03.5: problem 30
(2 points)
suppose $(0,-4)$ is a point on the graph of $y = f(x)$. what is a point that will be on the graph of $y=-f(x + 6)$?
help (points)
enter a point as $(a,b)$, including the parentheses.
preview my answers submit answers show me another
you have attempted this problem 0 times.
you have unlimited attempts remaining.
email instructor

Explanation:

Step1: Analyze the horizontal shift

For the function \(y = f(x + 6)\), the graph of \(y=f(x)\) is shifted 6 units to the left. If the original \(x\) - value is \(x = 0\) for \(y = f(x)\), for \(y=f(x + 6)\), we set \(x+6=0\), which gives \(x=-6\).

Step2: Analyze the vertical reflection

For the function \(y=-f(x + 6)\), after the horizontal shift, we take the negative of the \(y\) - value of \(f(x + 6)\). The original \(y\) - value for \(f(0)\) is \(- 4\). For \(y=-f(x + 6)\), when \(x=-6\) (from Step 1), \(y=-f(-6 + 6)=-f(0)\). Since \(f(0)=-4\), then \(y=-(-4)=4\).

Answer:

\((-6,4)\)