Rewrite each rational function in graphing form. Then graph it

Mathematics

1 answer:

Nadya [2.5K]3 years ago

3 0

Factor the top and bottom. vertical asymptotes are the values for x that will make the denominator = 0. To find the horizontal asymptote when the powers of the numerator and denominator are the same, just divide to coefficients.
asymptotes are where the graph cant go, the graph will get closer and closer by never touch....see the attachment

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2 years ago

The equation of a circle is x2 + y2 + 6x + 4y + 10 = 1. What is this equation written in its standard form?

Over [174]

You need to complete the square in x and in y,

$x^{2} + y^{2} + 6x + 4y + 10 = 1$

First, group the x-terms and the y-terms separately.

$x^{2} + 6x + y^{2} + 4y + 10 = 1$

Move the 10 to the right side by subtracting 10 from both sides.

$x^{2} + 6x + y^{2} + 4y = -9$

Now complete the square in x and in y.
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3 years ago

Which of the following statements best describes the effect of replacing the graph of y = f(x) with the graph of y = f(x + 6)? T

Alenkasestr [34]

Answer:

The graph of y = f(x) will shift left 6 units, as shown in figure a.

Step-by-step explanation:

A translation means we are able to move the graph of a function up or down - normally called Vertical Translation - and right or left - commonly called Horizontal Translation.

If we replace the graph of y = f(x) with the graph of y = f(x + 6). It means we have added 6 units to the input, meaning the graph y = f(x) will shift left by 6 units as 6 is being added directly to the x, so it is f(x + 6).

For example, if y = x² is the original function and of 6 is directly added to x i.e. f(x + 6), making it y = (x + 6)². So, we can easily observe that there will be a horizontal translation left of 8 units, as shown in figure a.

So, the graph of y = f(x) will shift left 6 units.

Keywords: graph shift, translation

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