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

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

Remember that the denominator cannot be equal to zero

so

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

Simplify the expression

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

so

For f(x)=0

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

Remember that the denominator cannot be equal to zero

so

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

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)

For x=-2

therefore

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

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

we have

Remember that the denominator cannot be equal to zero

so

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

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)

For x=1

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

so    

For f(x)=0

 -----> 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

Simplify the expression

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

Remember that the denominator cannot be equal to zero

so

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

Discontinuity at x=-1

Simplify the expression

For x=-1

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

Simplify the expression      

Remember that the denominator cannot be equal to zero

so

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

Discontinuity at x=2

Simplify the expression

Apply difference of squares

For x=2

therefore

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

what are the statments

step-by-step explanation: