Math  /  Algebra

QuestionTo graph the function g(x)=f(x+1)+4 g(x) = -f(x+1) + 4 , use the graph of y=f(x) y = f(x) provided.

Studdy Solution

STEP 1

1. The function g(x)=f(x+1)+4 g(x) = -f(x+1) + 4 is a transformation of the function y=f(x) y = f(x) .
2. Transformations include horizontal shifts, vertical shifts, and reflections.
3. We need to apply these transformations in the correct order to graph g(x) g(x) .

STEP 2

1. Identify the transformations applied to f(x) f(x) .
2. Apply the horizontal shift to the graph of y=f(x) y = f(x) .
3. Apply the reflection over the x-axis to the graph.
4. Apply the vertical shift to the graph.
5. Sketch the transformed graph.

STEP 3

Identify the transformations applied to f(x) f(x) in the function g(x)=f(x+1)+4 g(x) = -f(x+1) + 4 .
- The term (x+1) (x+1) inside the function indicates a horizontal shift. - The negative sign in front of f(x+1) f(x+1) indicates a reflection over the x-axis. - The +4 +4 outside the function indicates a vertical shift.

STEP 4

Apply the horizontal shift to the graph of y=f(x) y = f(x) .
- The expression f(x+1) f(x+1) indicates a shift to the left by 1 unit.

STEP 5

Apply the reflection over the x-axis to the graph.
- The negative sign in front of f(x+1) f(x+1) means that the graph is reflected over the x-axis. This means that every point (x,y) (x, y) on the graph of f(x+1) f(x+1) becomes (x,y) (x, -y) .

STEP 6

Apply the vertical shift to the graph.
- The +4 +4 indicates a vertical shift upwards by 4 units. This means that every point (x,y) (x, -y) on the reflected graph becomes (x,y+4) (x, -y + 4) .

STEP 7

Sketch the transformed graph.
- Start with the graph of y=f(x) y = f(x) . - Shift the graph 1 unit to the left. - Reflect the shifted graph over the x-axis. - Shift the reflected graph 4 units upward. - The resulting graph is g(x)=f(x+1)+4 g(x) = -f(x+1) + 4 .
The graph of g(x)=f(x+1)+4 g(x) = -f(x+1) + 4 is now sketched based on the transformations applied to y=f(x) y = f(x) .

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord