37.3k views
5 votes
practice help!What is the equation of g in terms of f?A. g(x) = f(x)B. g(x) = -f(x)C. g(x) = f(-x)D. g(x) = -f(-x)

practice help!What is the equation of g in terms of f?A. g(x) = f(x)B. g(x) = -f(x-example-1
User Charmee
by
8.8k points

1 Answer

6 votes

To answer this question, we can proceed as follows:

1. We can find the equation for the quadratic function, f(x) (solid line). To do this, we can use the vertex form of quadratic functions as follows:


f(x)=a(x-h)^2+k

Where (h, k) is the vertex of the parabola. From the graph, we have that the vertex is (1, -4). We can also see that the y-intercept of this quadratic function is (0, -3). Then with this information, we can find the equation of the function as follows:


f(x)=a(x-1)^2+(-4)\Rightarrow f(x)=a(x-1)^2-4

Now, to find the value of as follows:

1. f(0) = -3


-3=a(0-1)^2-4\Rightarrow-3=a(-1)^2-4\Rightarrow-3=a(1)-4

Then, we have:


-3=a-4\Rightarrow-3+4=a-4+4\Rightarrow1=a\Rightarrow a=1

Then, the equation of the function is:


f(x)=1(x-1)^2-4\Rightarrow f(x)=(x-1)^2-4

Now, to find the other function in terms of f(x), we can see that the function, g(x), is the result of reflecting f(x) in the y-axis, f(-x), and then reflecting the resulting function in the x-axis, -f(-x), as follows:

We have that the two functions are:


f(x)=(x-1)^2-4
g(x)=-f(-x)\Rightarrow g(x)=-((-x-1)^2-4)
g(x)=-(-x-1)^2+4

If we graph both functions, we have:

Therefore, the equation of g in terms of the function f is:


g(x)=-f(-x)

[Option D.]

practice help!What is the equation of g in terms of f?A. g(x) = f(x)B. g(x) = -f(x-example-1
practice help!What is the equation of g in terms of f?A. g(x) = f(x)B. g(x) = -f(x-example-2
User Heptadecagram
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories