Describe the vertical asymptote(s) and hole(s) for the graph of . y= (x-3) (x-1)/(x-)

The vertical line x = 5 is a vertical asymptote

There is a hole at (1, 1/2)

Aslo, see the explanation below and the graph attached.

Explanation:

The function is:

The vertical asymptotes happen at the points where the denominator equals zero (the function is undefined) and the limit of the function trends to + or - infinity.

If the denominator equals zero, but the limit of the function is defined, then that does not define an asymptote but a hole.

There are two points where the denominator is zero.  Those are:

Now, calculate both limits:

1) Limit when x → 5

Hence, the vertical line x = 5 is an asymptote.

2) Limit when x → 1

Hence, there is a hole at x = 1.

See the graph attached.

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step-by-step explanation:

f(x)=2x^2 -1 

translation is a function transformation that transform the function in a way of translating. by translating the function its graph is moved  up an down. moving the function f(x) 2 units to the left will be the new function g(x) with the equation: g(x)=f(x+2)=2(x+2)^2 -1