Which of the following is a transformati...

Which of the following is a transformation of y=f(x) that translates this function down 3, shrinks it horizontally by a factor of 2, and reflects it about the x-axis?

`y=-2f(x-3)`

`y=f(-2x)-3`

`y=-f((1)/(2)x)-3`

`y=-f(2x)-3`

Text Solution

Verified by Experts

The horizontal shrinking by a factor of 2 of is the multiplication of x by 2 before the function is applied. The reflection about the x-axis is the negation of the function after it is applied. The translation down 3 is the addition of -3 after the function is applied.

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For which of the following functions does f(x) f(2 - x) ?

`f(x) = x + 2`

`f(x) = 2x - x^2`

`f(x) = 2 - x`

`f(x) = (2 - x)^(2)`

In the figure above, the graph of y=f(x) has two transformations performed on it. First it is rotated 180^(@) about the origin, and then it is reflected about the x-axis. Which of the following is the equations of the resulting curve?

y=-f(x)

y=f(x+2)

x=f(y)

y=f(x)

Which of the following is horizontal asymptote to the function f(x)= (3x^4-7x^3+2x^2+1)/(2x^4-4) ?

y=-3.5

y=0

y=0.25

y=1.5