functions g(x) = x^2 + 6 The parent function f is: f(x)= x^2 Use function notation to write g in terms of f.
Answer: We are given the functions:
- g(x)=x2+6g(x) = x^2 + 6
- The parent function: f(x)=x2f(x) = x^2
We want to express g(x)g(x) in terms of f(x)f(x) using function notation.
Step 1: Identify the Relationship Between g(x)g(x) and f(x)f(x)
We see that g(x)g(x) is just f(x)f(x) plus 6. That is:
g(x)=f(x)+6g(x) = f(x) + 6
Step 2: Use Function Notation
Since f(x)=x2f(x) = x^2, we substitute f(x)f(x) into the equation:
g(x)=f(x)+6g(x) = f(x) + 6
Final Answer:
g(x)=f(x)+6g(x) = f(x) + 6
This notation shows that g(x)g(x) is obtained by taking the parent function f(x)f(x) and shifting it vertically by 6 units.
