I think the answer is B.
But my second choice would be C.
Answer:
y = 2x^2 − 4x + 5
y = 2(x^2 − 2x) + 5
y = 2(x^2 − 2x + 1 - 1) + 5
y = 2(x^2 − 2x + 1) + 5 - 2
y = 2(x - 1)^2 + 3
x = 1 is the axis of symmetry.
Do you agree?
First, you need to find the derivative of this function. This is done by multiplying the exponent of the variable by the coefficient, and then reducing the exponent by 1.
f'(x)=3x^2-3
Now, set this function equal to 0 to find x-values of the relative max and min.
0=3x^2-3
0=3(x^2-1)
0=3(x+1)(x-1)
x=-1, 1
To determine which is the max and which is the min, plug in values to f'(x) that are greater than and less than each. We will use -2, 0, 2.
f'(-2)=3(-2)^2-3=3(4)-3=12-3=9
f'(0)=3(0)^2-3=3(0)-3=0-3=-3
f'(2)=3(2)^2=3(4)-3=12-3=9
We examine the sign changes to determine whether it is a max or a min. If the sign goes from + to -, then it is a maximum. If it goes from - to +, it is a minimum. Therefore, x=-1 is a relative maximum and x=1 is a relative miminum.
To determine the values of the relative max and min, plug in the x-values to f(x).
f(-1)=(-1)^3-3(-1)+1=-1+3+1=3
f(1)=(1)^3-3(1)+1=1-3+1=-1
Hope this helps!!
Answer:
Option A) The function is even because it is symmetric with respect to the y-axis.
Step-by-step explanation:
We are given a graph of the function.
We can see that the given function is symmetric around the y axis as the y axis acts as a mirror.
Symmetry around y-axis
- The y-axis acts as the line of symmetry for the given graph.
- A graph is said to be symmetric about the y axis if (a,b) is on the graph, then we can find the point (-a,b) on the graph as well.
Even Function:
- A function is said to be even if

- A function f is even if the graph of f is symmetric with respect to the y-axis
Odd function:
- A function is said to be odd if

- A function f is even if the graph of f is symmetric with respect to the x-axis.
Thus, we can write that the given function is an even function as the the graph is symmetric to the y-axis.
Option A) The function is even because it is symmetric with respect to the y-axis.
Answer:
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Step-by-step explanation:
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