Question

Drag the tiles to the correct boxes to complete the pairs. Match the functions to their x-intercepts.

1) f(x)= log x-1
2) f(x)= -(log x-2)
3) f(x)= log (-x-2)
4) f(x)= -log -(x-1)
a) (0,0)
b) (-3,0)
c) (10,0)
d) (100,0)

Answer 1

See below in bold.

Explanation:

The x intercepts occur when f(x) = 0.

1. logx - 1 = 0

logx = 1

By the definition of a log ( to the base 10):

x = 10^1 = 10

So the x-intercept is c (10,0).

2. - (logx - 2) = 0

logx - 2 = 0

log x = 2

so x = 100.

So it is d (100,0).

3 . log(-x - 2) = 0

-x - 2 = 10^0 = 1

-x = 3

x = -3

So it is b (-3, 0).

4. f(x) = -log -(x - 1)

log - (x - 1) = 0

log 1 = 0

so -(x - 1) = 1

- x + 1 = 1

x = 1-1 = 0

So it is a. (0,0).

Answer 2

Function x-intercept

`f(x)=\log x-1`
`(10,0)`

`f(x)=-(\log x-2)`
`(100,0)`

`f(x)=\log (-x-2)`
`(-3,0)`

`f(x)=-\log -(x-1)`
`(0,0)`

Explanation:

We know that the x-intercept of a function is the point where the function value is zero.

i.e. the x where f(x)=0

1)

`f(x)=\log x-1`

when
`f(x)=0` we have:

`\log x-1=0\\\\i.e.\\\\\log x=1\\\\i.e.\\\\\log x=\log 10`

Hence, taking the exponential function on both the sides of the equation we have:

`x=10`

The x-intercept is: (10,0)

2)

`f(x)=-(\log x-2)`

when,
`f(x)=0`

we have:

`-(\log x-2)=0\\\\i.e.\\\\\log x-2=0\\\\i.e.\\\\\log x=2\\\\i.e.\\\\\log x=2\cdot 1\\\\i.e.\\\\\log x=2\cdot \log 10\\\\i.e.\\\\\log x=\log (10)^2`

Since,

`m\log n=\log n^m`

Hence, we have:

`\log x=\log 100`

Taking anti logarithm on both side we get:

`x=100`

Hence, the x-intercept is:

(100,0)

3)

`f(x)=\log (-x-2)`

when

`f(x)=0`

we have:

`\log (-x-2)=0\\\\i.e.\\\\\log (-x-2)=\log 1`

On taking anti logarithm on both the side of the equation we get:

`-x-2=1\\\\i.e.\\\\x=-2-1\\\\i.e.\\\\x=-3`

Hence, the x-intercept is: (-3,0)

4)

`f(x)=-\log -(x-1)`

when,

`f(x)=0\ we\ have:`

`-\log -(x-1)=0\\\\i.e.\\\\\log -(x-1)=0\\\\i.e.\\\\\log -(x-1)=\log 1\\\\i.e.\\\\-(x-1)=1\\\\i.e.\\\\x-1=-1\\\\i.e.\\\\x=-1+1\\\\i.e.\\\\x=0`

Hence, the x-intercept is: (0,0)