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2 years ago

Find f(2) and f(a+h) when f(x)=3x^2+2x+4

1 answer:

4 0

F(2) = 3(2)^2 + 2(2) + 4

= 3(4) + 4 + 4

= 12 + 8

f(2) = 20

f(a+h) = 3(a+h)^2 + 2(a+h) + 4

= 3(a^2 + 2ah + h^2) + 2a + 2h + 4

f(a+h) = 3a^2 + 6ah + 3h^2 + 2a + 2h + 4

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Step-by-step explanation:

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2 years ago

What is the shape of the graph of the function?<br> g(x)= 3/2 (2/3) ^x

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Answer:

Please check the attached graph.

From the graph, it is clear that option B is the correct option.

Step-by-step explanation:

Given the function

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Determining the y-intercept

We know that the value of the y-intercept can be determined by setting x = 0, and determining the corresponding value of y.

substituting x = 0 in the fuction

$y=\:\frac{3}{2}\:\left(\frac{2}{3}\right)^x$

$y=\:\frac{3}{2}\:\left(\frac{2}{3}\right)^0$

Apply rule: $a^0=1,\:a\ne \:0$

$y=1\cdot \frac{3}{2}$

$y=\frac{3}{2}$

$y = 1.5$

Therefore, the point representing the y-intercept is:

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Determining the x-intercept

We know that the value of the x-intercept can be determined by setting y = 0, and determining the corresponding value of x.

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$0=\frac{3}{2}\left(\frac{2}{3}\right)^x$

Using the zero factor principle

if ab=0, then a=0 or b=0 (or both a=0 and b=0)

$\left(\frac{2}{3}\right)^x=0$

We know that $a^{f\left(x\right)}$ can not be zero or negative for x ∈ R

Thus, NONE represents the x-intercept.

Please check the attached graph.

From the graph, it is clear that option B is the correct option.

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2 years ago

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