which of the following results in the graph of f(x)=xto the second powwer 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
The Subject is not 10th grade, etc. If you post the title correctly (math?) you will get the correct help sooner.
Sra
Id say... b
1/2 1/4 and 1/12
To determine which function will result in the graph of f(x)=x^2 being expanded vertically by a factor of 3 and reflected over the x-axis, we can break down the given options and examine the transformations involved.
A vertical expansion by a factor of 3 means that the y-coordinates of the original graph should be multiplied by 3, which implies that the function should have a coefficient of 3 in front of the x^2 term.
A reflection over the x-axis means that the positive and negative y-values of the original graph should be swapped. This is achieved by multiplying the entire function by -1.
Analyzing the options:
a. f(x) = (1/3)x^2 - This option does not have the correct coefficient of 3 in front of x^2.
b. f(x) = -3x^2 - This option has the correct coefficient of -3 in front of x^2 but does not reflect the graph over the x-axis.
c. f(x) = -(1/x^2) + 3 - This option does not have the correct form of the original function and does not involve the needed transformations.
d. f(x) = -(1/3)x^2 - This option has the correct coefficient of -(1/3) in front of x^2, resulting in a vertical expansion by a factor of 3. Additionally, the negative sign reflects the graph over the x-axis.
Therefore, the correct answer is d. f(x) = -(1/3)x^2.