Mathematics, 29.08.2019 12:10 MK100

Which exponential function has an x-intercept?
a. f(x) = 100x−5 − 1
b. f(x) = 3x−4 + 2
c. f(x) = 7x−1 + 1
d. f(x) = -8x+1 − 3

Answers: 2

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Answers

Answer from: tynitenaire

It would be C since it would be f(x) = 7x

Answer from: xlajbd

Option A - x-intercept is at (5,0)

Step-by-step explanation:

Given : Exponential Functions

To find : Which exponential function has an x-intercept?

Solution :

x-intercept is the value at which the value of y=0.

To find the x-intercept we have to substitute y=0 or f(x)=0

A. $f(x)=100^{x-5}-1$

x-intercept at f(x)=0

$0=100^{x-5}-1$

$100^{x-5}=1$

Taking log both side,

${x-5}\log 100=\log 1$

{x-5}(2)=0

x-5=0

x=5

Therefore, the x-intercept of the given function is (5,0).

B. $f(x)=3^{x-4}+2$

x-intercept at f(x)=0

$0=3^{x-4}+2$

$3^{x-4}=-2$

Taking log both side,

${x-4}\log 3=\log (-2)$

Since, log (-2) is not defined.

Therefore, the x-intercept of the given function is none.

C. $f(x)=7^{x-1}+1$

x-intercept at f(x)=0

$0=7^{x-1}+1$

$7^{x-1}=-1$

Taking log both side,

${x-1}\log 7=\log (-1)$

Since, log (-1) is not defined.

Therefore, the x-intercept of the given function is none.

D. $f(x)=-8^{x+1}-3$

x-intercept at f(x)=0

$0=-8^{x+1}-3$

$-8^{x+1}=3$

Taking log both side,

${x+1}\log (-8)=\log (3)$

Since, log (-8) is not defined.

Therefore, the x-intercept of the given function is none.

Hence, Option A has only x-intercept.

Answer from: Quest

2x^2 -2x -12 = 02(x -3)(x +2) = 0see below for explanation

step-by-step explanation:

equation

you are asked to write the equation

expression = 0

using the given expression. when you do that, you have

2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

(x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

-6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

x - 3 = 0

x = 3 . . . add 3 to both sides of the equation

x +2 = 0

x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

Answer from: Quest

i dont know i just need points