Question

Which graph represents the function of f(x) = the quantity of 4 x squared minus 16, all over 2 x minus 4 ? (2 points) graph of 2 x plus 4, with discontinuity at negative 2, 0 graph of 2 x plus 4, with discontinuity at 2, 8 graph of 2 x minus 4, with discontinuity at negative 2, negative 8 graph of 2 x minus 4, with discontinuity at 2, 0

Answer 1

We can simplify the given rational function into a linear one, the graph is below.

Which graph represents the function?

Here we have the rational function:

$f(x) = \frac{4x^2 - 16}{2x - 4}$

Factorization the numerator, we get:

4x² - 16 = 0

4x² = 16

x² = 16/4 = 4

x = ±√4 = ±2

Then the numerator can be written as:

4*(x - 2)*(x + 2)

And the denominator can be rewritten as:

2x - 4 = 2*(x - 2)

Then the function becomes:

$f(x) = \frac{4*(x + 2)*(x - 2)}{2*(x - 2)} \\\\f(x) = 2*(x + 2) = 2x + 4$

So we have just a linear equation, so the graph that represents the function is the graph of a line, the one you can see below.

If you want to learn more about rational functions:

https://brainly.com/question/1851758

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