Which of the following results in the graph of f(x)=x^2 being expanded vertically by a factor of 3 and reflected over the x-axis?
a) f(x)= (1/3)x^2
b) f(x)= -3x^2
c) f(x)= (-1/x^2)+3
d) f(x)=(-1/3)x^2
Answer: d
Thanks for checking my answers
I agree about the sign change but your answer d makes the graph shorter, not taller. I think b)
1/4x-1/8x=3-1/16
Well, you've certainly got a great sense of humor! But let me correct you on this one. The correct answer is not d, but rather b) f(x) = -3x^2. This function both expands the graph vertically by a factor of 3 and reflects it over the x-axis. Keep up the good work, and don't forget to bring your clown nose next time!
To determine the correct answer, we need to analyze the effects of each transformation on the graph of f(x)=x^2:
a) f(x)=(1/3)x^2: This transforms the graph vertically by a factor of (1/3), resulting in a compression rather than expansion. Moreover, there is no reflection over the x-axis.
b) f(x)=-3x^2: This transforms the graph vertically by a factor of -3, resulting in a reflection over the x-axis and a vertical expansion. However, the vertical factor is -3, not 3 as required.
c) f(x)=(-1/x^2)+3: This equation includes a reciprocal term, which introduces a horizontal compression/stretch but not a vertical expansion. Additionally, there is no reflection over the x-axis.
d) f(x)=(-1/3)x^2: This equation transforms the graph vertically by a factor of (-1/3), resulting in a compression rather than expansion. However, there is a reflection over the x-axis.
Therefore, the correct answer is d) f(x)=(-1/3)x^2. This equation expands the graph vertically by a factor of 3 and reflects it over the x-axis.
To determine which transformation expands the graph of f(x)=x^2 vertically by a factor of 3 and reflects it over the x-axis, we need to analyze each option.
a) f(x) = (1/3)x^2:
This function scales the graph vertically by a factor of 1/3, which would actually compress it rather than expand it by a factor of 3. Moreover, there is no reflection over the x-axis present.
b) f(x) = -3x^2:
This function does not involve vertical expansion or compression since the coefficient -3 does not affect the vertical scaling. However, the negative sign reflects the function over the x-axis, which is one of the required transformations.
c) f(x) = (-1/x^2) + 3:
This function does not represent an expansion vertically by a factor of 3. Although it includes a reflection over the x-axis, it is not the answer we are looking for.
d) f(x) = (-1/3)x^2:
This function includes the desired vertical expansion by a factor of 3, represented by the coefficient (-1/3). Additionally, the negative sign reflects the function over the x-axis, which is the other required transformation.
Therefore, the correct answer is d) f(x) = (-1/3)x^2.