Exploring Linear Transformations

The video tutorial covers linear transformations, focusing on how changes in equations affect the graph of a function. It explains the impact of multiplying a function by a constant, both outside and inside parentheses, on the steepness and direction of the graph. The tutorial also discusses how adding or subtracting constants shifts the graph vertically or horizontally. Examples are provided to illustrate these concepts, and a summary reinforces the key points.

What happens to the graph of a linear equation if you change the y-intercept?

• The placement of the line changes.

• The line becomes a curve.

• The direction of the line changes.

• The steepness of the line changes.

If G(x) = 2f(x) and f(x) = x, what is G(x)?

• G(x) = 2x

• G(x) = -2x

• G(x) = x

• G(x) = x/2

What effect does multiplying f(x) by a number greater than 1 have on the graph?

• It makes the graph less steep.

• It shifts the graph up.

• It shifts the graph down.

• It makes the graph steeper.

If G(x) = f(5x), what happens to the graph of f(x)?

• It becomes less steep.

• It shifts down.

• It becomes steeper.

• It shifts up.

What happens to the graph if the number inside the parentheses is less than 1?

• The graph becomes steeper.

• The graph becomes less steep.

• The graph shifts up.

• The graph shifts down.

If G(x) = f(x + 1), what happens to the graph of f(x)?

• It shifts up by 1 unit.

• It shifts right by 1 unit.

• It shifts down by 1 unit.

• It shifts left by 1 unit.

What does a negative sign inside the parentheses indicate?

• The graph shifts right.

• The graph shifts down.

• The graph shifts up.

• The graph shifts left.

If G(x) = f(x) + 2, what happens to the graph of f(x)?

• It shifts right by 2 units.

• It shifts left by 2 units.

• It shifts down by 2 units.

• It shifts up by 2 units.

What happens to the graph if a constant is subtracted outside the function?

• The graph shifts down.

• The graph shifts up.

• The graph shifts right.

• The graph shifts left.

If G(x) = f(x) - 4, what happens to the graph of f(x)?

• It shifts left by 4 units.

• It shifts right by 4 units.

• It shifts down by 4 units.

• It shifts up by 4 units.