MATH SOLVE

3 months ago

Q:
# Match the functions to their x-intercepts.f(x) = log x – 1f(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

Accepted Solution

A:

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)