Graph Transformations and Effects

The video tutorial explains how graphs can be transformed using different values. It introduces the parent function f(x) = x and discusses how the A, C, and D values affect the graph's steepness, direction, and position. The A value changes the steepness, the C value shifts the graph left or right, and the D value shifts it up or down. An example is provided with G(x) = -1/2x + 3, illustrating these transformations, including reflection over the x-axis and shifts. The video concludes with a summary of these concepts.

What is the parent function in the context of graph transformations?

• f(x) = x

• f(x) = x^2

• f(x) = x^3

• f(x) = 1/x

How does an 'a' value greater than 1 affect the graph?

• Makes the graph less steep

• Makes the graph steeper

• Shifts the graph to the right

• Shifts the graph to the left

What does a positive 'C' value indicate in terms of graph movement?

• Shift to the left

• Shift downwards

• Shift to the right

• Shift upwards

If the equation is x - 5, in which direction does the graph shift?

• Left 5 units

• Down 5 units

• Right 5 units

• Up 5 units

What does a positive 'D' value do to the graph?

• Reflects the graph over the x-axis

• Shifts the graph down

• Shifts the graph up

• Reflects the graph over the y-axis

What is the effect of a positive 'D' value in the context of graph transformations?

• Shift up

• Shift left

• Shift right

• Shift down

In the new example, what does a negative 'a' value cause?

• The graph becomes steeper

• The graph shifts to the right

• The graph reflects over the x-axis

• The graph shifts upwards

What is the effect of an 'a' value between 0 and 1?

• The graph becomes less steep

• The graph shifts to the left

• The graph becomes steeper

• The graph shifts downwards

How does the graph of G(x) compare to f(x) in terms of steepness when a = 1/2?

• G(x) is inverted

• G(x) is the same steepness

• G(x) is less steep

• G(x) is steeper

What does the negative sign in front of 'a' indicate?

• The graph reflects over the y-axis

• The graph shifts up

• The graph shifts down

• The graph reflects over the x-axis