Understanding Function Transformations

The video tutorial explains how to graph functions g(x) = -2f(x) and h(x) = f(1/3x) based on the graph of f(x) = x. It covers the effects of scaling and flipping the graph over the x-axis for g(x), and the horizontal scaling for h(x). The tutorial provides step-by-step examples to illustrate these transformations.

What is the initial function f(x) defined as in the video?

• f(x) = -x

• f(x) = x^2

• f(x) = x

• f(x) = 2x

How is g(x) related to f(x) in the video?

• g(x) = 2 * f(x)

• g(x) = f(x) + 2

• g(x) = -f(x)

• g(x) = -2 * f(x)

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CCSS.HSF.IF.A.2

What is the value of g(3) if f(x) = x?

• -3

• 3

• 6

• -6

What happens to the graph of f(x) when it is multiplied by -2?

• It flips over the x-axis and scales by a factor of 2.

• It shifts up by 2 units.

• It remains unchanged.

• It shifts down by 2 units.

What is the effect of multiplying f(x) by a negative number?

• It shifts the graph downwards.

• It makes the graph narrower.

• It flips the graph over the x-axis.

• It shifts the graph to the left.

What is the new function h(x) defined as in the video?

• h(x) = f(3x)

• h(x) = f(x/3)

• h(x) = f(1/3 * x)

• h(x) = 3 * f(x)

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CCSS.HSF.IF.A.1

If f(2) = 2, what is h(6) when h(x) = f(1/3 * x)?

• 1

• 6

• 2

• 3

What is the effect of multiplying x by a fraction in the function h(x)?

• It makes the graph narrower.

• It shifts the graph to the right.

• It makes the graph wider.

• It flips the graph over the y-axis.

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CCSS.HSF.IF.A.1

CCSS.8.F.A.1

What is the value of h(9) if f(-3) = -3 and h(x) = f(1/3 * x)?

• -9

• 9

• -3

• 3

How does multiplying x by a value greater than one affect the graph?

• It makes the graph wider.

• It makes the graph narrower.

• It flips the graph over the x-axis.

• It shifts the graph upwards.