Question

How does changing the function from f(x) = 2 sin 4x to g(x) = 2 sin 4x + 3 affect the range of the function?

The function shifts up 3 units, so the range changes from −2 to 2 in f(x) to 1 to 5 in g(x).

The function shifts up 3 units, so the range changes from −1 to 1 in f(x) to 2 to 4 in g(x).

The function shifts up 4 units, so the range changes from −2 to 2 in f(x) to 2 to 6 in g(x).

The function shifts up 4 units, so the range changes from −1 to 1 in f(x) to 3 to 5 in g(x).

Answer 1

@beccaboo333

Answer 2

@Destinymasha @nincompoop

Answer 3

Have you tried graphing both functions? If you have a graphing calculator, that should be relatively easy to do. Once you have the pertinent graphs, you can easily compare them visually.

Find the range of the original function.

Then, modify this range by adding 3 to both upper and lower limit on y.

Answer 4

What are the period and phase shift for f(x) = 5 tan(2x − π)?

period: π; phase shift: x = pi over two

period: π; phase shift: x = negative pi over two

period: pi over two; phase shift: x = negative pi over two

period: pi over two; phase shift: x = pi over two

Answer 5

@ranga

Answer 6

Have you found the answer for the first question?

Answer 7

Yeah! @ranga

Answer 8

f(x) = 5 tan(2x − π)
Put it in form: A*tan(B(x - C)) where A is amplitude; period = pi/B; phase shift = C.

f(x) = 5 tan(2x − π)
The coefficient of x is 2. You have to factor out the 2 to make the coefficient of x one.
f(x) = 5 tan(2(x − π/2)). A = 5, B = 2, C = π/2
Period = pi/B = ?
Phase shift = C = ?

Answer 9

What is the rate of change for f(x) = 4 sin x − 2 on the interval from x = 0 to x = pi over 2?

pi over 4

4 over pi

pi over 8

8 over pi

Answer 10

@ranga

Answer 11

Average rate of change of f(x) in the interval [a,b] = (f(b) - f(a)) / (b - a)

Answer 12

Would it be set up as f(pi/2) - f(0)/(pi/2)

Answer 13

Yes.
\[
\Large
\frac{f(\pi / 2) - f(0)}{\pi /2} = \frac{\{4\sin(\pi / 2) - 2\}- \{4\sin(0) - 2\}}{\pi /2} = \ ?
\]