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3 years ago

11

Which statement describes the function y = axn when a = 1 and n is even?

2 answers:

Vera_Pavlovna [14]3 years ago

3 0

Hello,

y=ax^n
a=1
n=2k

f(x)=y=x^(2k)

A:
y'=2k*x^(2k-1)
if x<0 y'<0
if x>0 y'>0 ==>opens upwise

f(-1)=(-1)^(2k)=1
f(0)=0^(2k)=0
f(1)=1^(2k)=1 C is exact

y=x² has one intercept with x axis.

Answer C

f(-x)=(-x)^(2k)=((-x)^2)k=(x²)^k=x^(2k)
The graph is symmetric about y axis

Naya [18.7K]3 years ago

3 0

Answer: C

The graph passes through (–1, 1), (0, 0), and (1, 1).

Step-by-step explanation:

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What degree of rotation is represented on this matrix

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Answer:

Option B is correct

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Step-by-step explanation:

A rotation matrix is a matrix that is used to perform a rotation in Euclidean space.

To find the degree of rotation using a standard rotation matrix i.e,

$R = \begin{bmatrix}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}$

Given the matrix: $\begin{bmatrix}0 & 1 \\ -1 & 0\end{bmatrix}$

Now, equate the given matrix with standard matrix we have;

$\begin{bmatrix}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}$ = $\begin{bmatrix}0 & 1 \\ -1 & 0\end{bmatrix}$

On comparing we get;

$\cos \theta = 0$ and $-\sin \theta =1$

As,we know:

$\cos \theta = \cos(-\theta)$

$\sin(-\theta) = -\sin \theta$

$\cos \theta = \cos(90^{\circ}) = \cos( -90^{\circ})$

we get;

$\theta = -90^{\circ}$

and

$\sin \theta =- \sin (90^{\circ}) = \sin ( -90^{\circ})$

we get;

$\theta = -90^{\circ}$

Therefore, the degree of rotation is, $-90^{\circ}$

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3 years ago