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AnnZ [28]
3 years ago
9

Which of the following functions have graphs that contain vertical asymptotes?

Mathematics
1 answer:
pshichka [43]3 years ago
6 0
A vertical asymptotic is a point at which y approaches positive or negative infinite, or both, and y is undefined at that x value.

Of the options, the reciprocal has a vertical asymptote. When approaches zero, y approaches 1÷0, or infinite.
The logarithmic function also has a vertical asymptote at x=0. Let's use f(x) =log base 10 (x) as an example. This function describes the exponent you'd have to put on 10 to get x. When x=0, we have a bit of a problem. What power can you raise 10 to to get 0? The answer is negative infinite, which would be
1/ (10^∞) = 0.

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Answer:

Since the lines are Perpendicular..

The Product of their Gradients = -1

m'm"=-1

m' from y=3x - 5 is 3

3.m" = -1

m" = -1/3.

Since Intercept on y axis = -2...

That of x at that point is =0

y-y' = m"(x-x")

y-(-2) = -1/3( x - 0)

y+2 = -1/3(x)

Multiplying through by 3

3y + 6 = -x

3y + x = -6. This is your Equation

To verify this.

Let's turn it into the Intercept form which is

x/a + y/b = 1

To get 1 at the right hand side... Divide through by -6

3y/-6 + x/-6 = 1

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You could see directly below y is its intercept and thats -2

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