Answer:
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
∴ [tex]10^{b}=a[/tex]
* 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
∴ [tex]10^{1}=x[/tex]
∴ 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
∴ [tex]10^{2}=(x)[/tex]
∴ 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
∴ [tex]10^{0}=(-x-2)[/tex] ⇒ 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
∴ [tex]10^{0}=-(x-1)[/tex] ⇒ 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)
