Match the functions to their x-intercepts.
f(x) = log x – 1
f(x) = -(log x – 2)
f(x) = log(-x – 2)
f(x) = -log -(x – 1)
(0, 0)
arrowboth
(-3, 0)
arrowboth
(10, 0)
arrowboth
(100, 0)
arrowboth

f(x) = log x – 1 ⇒  x-intercept = (10 , 0)

f(x) = -(log x – 2) ⇒ x-intercept = (100 , 0)

f(x) = log(-x – 2) ⇒ x-intercept = (-3 , 0)

f(x) = -log -(x – 1) ⇒ x-intercept = (0 , 0)

Step-by-step explanation:

* lets talk about the log

- If log a = b, that means the base of the log is 10

- To solve it we will change it to exponential function

∴

* Now do that in each one of the problem

* ∵ f(x) = log x - 1

- To find the x-intercept put y = 0

∴ log x - 1 = 0 ⇒ add 1 to both sides

∴ log x = 1 ⇒ change it to exponential function

∴

∴ x = 10

* The x-intercept = (10 , 0)

* ∵ f(x) = -(log x - 2)

- To find the x-intercept put y = 0

∴ -(log x - 2) = 0 ⇒ Multiply both sides by -1

∴ log x - 2 = 0 ⇒ add 2 to the both sides

∴ log x = 2 ⇒ change it to exponential function

∴

∴ x = 100

* The x-intercept = (100 , 0)

* ∵ f(x) = log (-x - 2)

- To find the x-intercept put y = 0

∴ log (-x - 2) = 0 ⇒ change it to exponential function

∴ ⇒ any number to the power of zero = 1 except 0

∴ -x - 2 = 1 ⇒ add 2 to the both sides

∴ -x = 3 ⇒ multiply both sides by -1

∴ x = -3

* The x-intercept = (-3 , 0)

* ∵ f(x) = -log -(x - 1)

- To find the x-intercept put y = 0

∴ -log -(x - 1) = 0 ⇒ multiply both sides by -1

∴ log -(x - 1) = 0 ⇒ change it to exponential function

∴ ⇒ any number to the power of zero = 1 except 0

∴ -(x - 1) = 1 ⇒ multiply both sides by -1

∴ x - 1 = -1 ⇒ add 1 to both sides

∴ x = 0

* The x-intercept = (0 , 0)