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3 years ago

Which of the following is a horizontal stretch of the parent function?

Mathematics

2 answers:

dlinn [17]3 years ago

8 0

Answer:

The correct option is 3.

Step-by-step explanation:

The parent function is

$f(x)=|x|$

The horizontal stretch and compression is defined as

$g(x)=|bx|$

If 0<b<1, then it is horizontal stretch and if b>1, then it is horizontal compression.

Graph 1 passing thought the point (1,-1).

$-1=|b(1)|$

This statement is false for any value of b, because the value of modulus can not be negative.

Graph 2 passing thought the point (1,2).

$2=|b(1)|$

$2=b$

Since b>1, therefore this graph represent the horizontal compression.

Graph 3 passing thought the point (2,1).

$1=|b(2)|$

$\frac{1}{2}=b$

Since 0<b<1, therefore this graph represent the horizontal stretch.

Thus, the correct option is 3.

melisa1 [442]3 years ago

6 0

Answer:

Step-by-step explanation:

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Choose whether it's always, sometimes, never

Keith_Richards [23]

Answer: An integer added to an integer is an integer, this statement is always true. A polynomial subtracted from a polynomial is a polynomial, this statement is always true. A polynomial divided by a polynomial is a polynomial, this statement is sometimes true. A polynomial multiplied by a polynomial is a polynomial, this statement is always true.

Explanation:

The closure property of integer states that the addition, subtraction and multiplication is integers is always an integer.

If $a\in Z\text{ and }b\in Z$ , then a+b\in Z.

Therefore, an integer added to an integer is an integer, this statement is always true.

A polynomial is in the form of,

$p(x)=a_nx^n+a_{n-1}x^{x-1}+...+a_1x+a_0$

Where $a_n,a_{n-1},...,a_1,a_0$ are constant coefficient.

When we subtract the two polynomial then the resultant is also a polynomial form.

Therefore, a polynomial subtracted from a polynomial is a polynomial, this statement is always true.

If a polynomial divided by a polynomial then it may or may not be a polynomial.

If the degree of numerator polynomial is higher than the degree of denominator polynomial then it may be a polynomial.

For example:

$f(x)=x^2-2x+5x-10 \text{ and } g(x)=x-2$

Then $\frac{f(x)}{g(x)}=x^2+5$ , which a polynomial.

If the degree of numerator polynomial is less than the degree of denominator polynomial then it is a rational function.

For example:

$f(x)=x^2-2x+5x-10 \text{ and } g(x)=x-2$

Then $\frac{g(x)}{f(x)}=\frac{1}{x^2+5}$ , which a not a polynomial.

Therefore, a polynomial divided by a polynomial is a polynomial, this statement is sometimes true.

As we know a polynomial is in the form of,

$p(x)=a_nx^n+a_{n-1}x^{x-1}+...+a_1x+a_0$

Where $a_n,a_{n-1},...,a_1,a_0$ are constant coefficient.

When we multiply the two polynomial, the degree of the resultand function is addition of degree of both polyminals and the resultant is also a polynomial form.

Therefore, a polynomial subtracted from a polynomial is a polynomial, this statement is always true.

3 0

3 years ago

Read 2 more answers

Solution q-2r=4<br> q+r=37

GenaCL600 [577]

Q-2r=4, therefore: q=4+2r.

Plug the value of q into q+r=37, so you get:

4+2r+r=37

3r=37-4=33

3r=33

Therefore: r=11.

q-2r=4, but r=11, so:

q-2(11)=4

q-22=4

Therefore q=26.

Check if the answer is correct using second equation:

q=4+2r=4+2(11)=4+22=26.

So: q=26 and r=11.

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3 years ago

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Tom [10]

Answer: 288

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Which is the parent function of y=√5x+6

Ostrovityanka [42]

Hi there! The answer is D.

The parent function is the simplest form of a function. We can distinguish a variety of parent functions like linear, exponential, square root, absolute, logarithmic, quadratic, cubic, rational or constant (trigonometric functions excluded).

Now we can have a look at the function.
$y = \sqrt{5x + 6}$

The thing that is the most important in this function is the square root, because this mainly decides the way the function looks. Therefore, the parent function is the simplest form of a square root function, which is the following:
$y = \sqrt{x}$

Therefore the answer is D.
~ Hope this helps you!

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3 years ago