Question

Find the x- and y-intercepts of the function f(x) = log(2x + 1) − 1. The x-intercept of the function f(x) = log(2x + 1) − 1 is __ . Its y-intercept is __.

1) (9.5,0)

(4.5,0)

(-9.5,0)

(-4.5,0)


2) (0,3)

(0,1)

(0,-3)

(0,-1)

Answer 1

1. (4.5,0)

2. (0,-1)

Explanation:

The intercept with the y-axis is making 0 the value of x and the intercept with the y-axis is making or the value of y.

a) If
`y=f(x)=log(2x+1)-1`

we make y=0

`0=log(2x+1)-1\\10^1=10^(log(2x+1))\\10=2x+1\\x=(9)/(2)=4.5`

Then the x-intercept is (4.5,0)

we make x=0

`log(2*0+1)-1=log(1)-1==-1y`

Then the y-intercept is (0,-1).