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3 years ago

Find f(4) for f(x) = 4x + 3. f(4) =

Mathematics

1 answer:

adell [148]3 years ago

3 0

Answer:

f(4) = 19

Step-by-step explanation:

Since we are given f(4), we substitute the x values with the number 4.

f(x) = 4x + 3

f(4) = 4(4) + 3

After substituting the x values with 4, solve the equation normally.

f(4) = 16 + 3

f(4) = 19

Our final answer is f(4) = 19

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3 years ago

Consider parent function f(x)=e^x and the transformes function g(x)= -1/2e^3x+4, quantitatively explain the transformations to t

kolezko [41]

Answer: reflection across the x-axis

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horizontal shrink by a factor of 1/3

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<u>Step-by-step explanation:</u>

$\text{Note:}\ g(x) = -Ae^{Bx-C}+D\\\bullet \quad \text{- represents a reflection across the x-axis}\\\\\bullet \quad \text{A represent a vertical stretch by a factor of A (shrink if}\ |A| < 1)\\\\\bullet \quad \text{B represents a horizontal stretch by a factor of}\ \dfrac{1}{B}\ (\text{shrink if}\ |B| >1) \\\\\bullet \quad \text{C represents a horizontal shift of C units}\ (\text{+ is right, - is left}) \\\\\bullet \quad \text{D represents a vertical shift of D units}\ (\text{+ is up, - is down})$

$\text{Parent function:}\ f(x)=e^x\\\text{Transformed function:}\ g(x)=-\dfrac{1}{2}e^{3x}+4\\$

The transformed function has the following:

Negative: reflection across the x-axis

A = 1/2 vertical shrink by a factor of 1/2

B = 3 horizontal shrink by a factor of 1/3

C = 0 no horizontal shift

D = 4 vertical shift of 4 units up

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