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3 years ago

The function f(x)=5(2)^x was replaced with f(x)+k , resulting in the function graphed below.

Mathematics

2 answers:

ella [17]3 years ago

5 0

In this problem, you have to find the y- intercept of $f(x)=5(2)^x$ . I graphed mine into a graphing calculator. An algebraic way to find it is to input x=0 in the function. The y-intercept is 5. You can see the y-intercept for the new one is -2. That means we shifted the graph down 7 units. (Vertical Shift down 7)
k=-7

Arisa [49]3 years ago

4 0

When x = 0 you get the y intercept y = 5
So the new fction goes from 5 to -2 , i.e. 7 units down, so k is -7

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3 years ago

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4 years ago

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3 0

3 years ago

Simplify this expression

kompoz [17]

The first step for solving this problem is to know that in order to divide by a fraction,, we must multiply by the reciprocal of that fraction. This will look like the following:
$\frac{x+2}{ x^{2} -6x-16}$ × 9x
Write -6x as a difference.
$\frac{x+2}{ x^{2} +2x-8x-16}$ × 9x
Factor out x from x² + 2x.
$\frac{x+2}{ x X (x+2)-8x-16}$ × 9x
Factor out -8 from -8(x + 2).
$\frac{x+2}{ x X (x+2)-8(x+2)}$ × 9x
Factor out x + 2 from the denominator (bottom) of the expression.
$\frac{x+2}{(x+2)X(x-8)}$ × 9x
Reduce the fraction with x + 2
$\frac{1}{x-8}$ × 9x
Finally,, calculate the product to find your final answer.
$\frac{9x}{x-8}$
This means that the correct answer to your question is going to be option B.
Let me know if you have any further questions.
:)

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3 years ago