section 03.5: problem 30\n(2 points)\nsuppose $(0,-4)$ is a point on the graph of $y = f(x)$. what is a…

section 03.5: problem 30\n(2 points)\nsuppose $(0,-4)$ is a point on the graph of $y = f(x)$. what is a point that will be on the graph of $y=-f(x + 6)$?\nhelp (points)\nenter a point as $(a,b)$, including the parentheses.\npreview my answers submit answers show me another\nyou have attempted this problem 0 times.\nyou have unlimited attempts remaining.\nemail instructor

section 03.5: problem 30\n(2 points)\nsuppose $(0,-4)$ is a point on the graph of $y = f(x)$. what is a point that will be on the graph of $y=-f(x + 6)$?\nhelp (points)\nenter a point as $(a,b)$, including the parentheses.\npreview my answers submit answers show me another\nyou have attempted this problem 0 times.\nyou have unlimited attempts remaining.\nemail instructor

Answer

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))