Mathematics, 07.01.2020 00:31 caylah6101

What are the zero(s) of the function f(x) = the quantity of 5 x squared minus 25 x, all over x ? (2 points)

x = 5

x = 0 and x = 5

x = 0

x = −5
2.
(05.06)
what is the discontinuity of the function f(x) = the quantity of x squared minus 4 x minus 12, all over x plus 2 ? (2 points)

(−6, 0)

(6, 0)

(−2, −8)

(2, −4)
3.
(05.06)
what is the discontinuity and zero of the function f(x) = the quantity of 3 x squared plus x minus 4, all over x minus 1 ? (2 points)

discontinuity at (−1, 1), zero at ( four thirds , 0)

discontinuity at (−1, 1), zero at ( negative four thirds , 0)

discontinuity at (1, 7), zero at ( four thirds , 0)

discontinuity at (1, 7), zero at ( negtive four thirds , 0)
4.
(05.06)
which graph represents the function of f(x) = the quantity of 4 x squared minus 4 x minus 8, all over 2 x plus 2 ? (2 points)

graph of 2 x minus 4, with discontinuity at negative 1, negative 6

graph of 2 x minus 4, with discontinuity at 1, negative 2

graph of 2 x plus 2, with discontinuity at negative 1, 0

graph of 2 x plus 2, with discontinuity at 1, 4
5.
(05.06)
which graph represents the function of f(x) = the quantity of 4 x squared minus 16, all over 2 x minus 4 ? (2 points)

graph of 2 x plus 4, with discontinuity at negative 2, 0

graph of 2 x plus 4, with discontinuity at 2, 8

graph of 2 x minus 4, with discontinuity at negative 2, negative 8

graph of 2 x minus 4, with discontinuity at 2, 0

Answers: 2

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Answers

Answer from: shannydouglas

Part 1) x=5

Part 2) (-2,-8)

Part 3) Discontinuity at (1,4), zero at (negative one third,0)

Part 4) Graph of 2x minus 4, with discontinuity at negative 1, negative 6

Part 5) Graph of 2x plus 4, with discontinuity at (2,8)

Step-by-step explanation:

Part 1) What are the zero(s) of the function f(x) ?

we have

$f(x)=\frac{5x^2-25x}{x}$

Remember that the denominator cannot be equal to zero

The function f(x) has a discontinuity at x=0

Simplify the expression

$f(x)=\frac{5x(x-5)}{x}$

f(x)=5(x-5)

The zeros of the function is the value of x when the value of the function is equal to zero

For f(x)=0

0=5(x-5)

therefore

x-5=0

x=5 ----> is a zero of the function

Part 2) What is the discontinuity of the function f(x)

we have

$f(x)=\frac{x^{2}-4x-12}{x+2}$

Remember that the denominator cannot be equal to zero

find the value of x for which the denominator is equal to zero

$x+2=0\\x=-2$

The value of x=-2 is a discontinuity

Simplify the expression above

Find the factors of the numerator (using a graphing tool see the attached figure N 1)

$f(x)=\frac{x^{2}-4x-12}{x+2}=\frac{(x+2)(x-6)}{x+2}=x-6$

f(x)=x-6

For x=-2

f(-2)=-2-6=-8

therefore

The discontinuity is the point (-2,-8)

Part 3) What is the discontinuity and zero of the function f(x)

we have

$f(x)=\frac{3x^{2}+x-4}{x-1}$

Remember that the denominator cannot be equal to zero

find the value of x for which the denominator is equal to zero

$x-1=0\\x=1$

The value of x=1 is a discontinuity

Simplify the expression above

Find the factors of the numerator (using a graphing tool see the attached figure N 2)

$f(x)=\frac{3(x+\frac{1}{3})(x-1)}{x-1}$

$f(x)=3(x+\frac{1}{3})$

For x=1

$f(1)=3(1+\frac{1}{3})$

f(1)=4

The discontinuity is the point (1,4)

The zeros of the function is the value of x when the value of the function is equal to zero

For f(x)=0

$0=3(x+\frac{1}{3})$

$x=-\frac{1}{3}$ -----> is a zero of the function

therefore

Discontinuity at (1,4), zero at (negative one third,0)

Part 4) Which graph represents the function of f(x)

we have

$f(x)=\frac{4x^{2}-4x-8}{2x+2}$

Simplify the expression

$f(x)=\frac{4(x^{2}-x-2)}{2(x+1)}$

$f(x)=\frac{2(x^{2}-x-2)}{(x+1)}$

Find the factors of the numerator (using a graphing tool see the attached figure N 3)

$f(x)=\frac{2(x+1)(x-2)}{(x+1)}$

Remember that the denominator cannot be equal to zero

find the value of x for which the denominator is equal to zero

$x+1=0\\x=-1$

Discontinuity at x=-1

Simplify the expression

f(x)=2(x-2)=2x-4

For x=-1

f(-1)=2(-1-2)=-6

discontinuity at (-1,-6)

therefore

Graph of 2x minus 4, with discontinuity at negative 1, negative 6

Part 5) Which graph represents the function of f(x)

we have

$f(x)=\frac{4x^{2}-16}{2x-4}$

Simplify the expression

$f(x)=\frac{4(x^{2}-4)}{2(x-2)}$

$f(x)=\frac{2(x^{2}-4)}{(x-2)}$

Remember that the denominator cannot be equal to zero

find the value of x for which the denominator is equal to zero

$x-2=0\\x=2$

Discontinuity at x=2

Simplify the expression

$f(x)=\frac{2(x^{2}-4)}{(x-2)}$

Apply difference of squares

$f(x)=\frac{2(x+2)(x-2)}{(x-2)}$

f(x)=2(x+2)=2x+4

For x=2

f(2)=2(2)+4=8

therefore

Graph of 2x plus 4, with discontinuity at (2,8)

What are the zero(s) of the function f(x) = the quantity of 5 x squared minus 25 x, all over x ? (2

Answer from: Quest

the answer is d

step-by-step explanation:

Answer from: Quest

step-by-step explanation:

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