Graph Transformations and Function Behavior

The video tutorial explains how adding a constant to a function, specifically f(x) = 5 * 2^x, affects its graph. By adding 5 to f(x), the graph shifts to the left. The tutorial uses specific x values to demonstrate this shift and explains that the transformation does not change the rate of increase but makes larger values appear sooner. The concept of shifting a graph by adding a constant is thoroughly analyzed and explained.

What happens to the graph of f(x) = 5 * 2^x when 5 is added to the function?

• It shifts to the left.

• It moves upwards.

• It moves downwards.

• It shifts to the right.

When the function f(x) = 5 * 2^x is modified to f(x + 5), what does the '+5' indicate?

• An increase in slope.

• A shift to the left.

• A shift to the right.

• A decrease in slope.

If x = 0 in the original function f(x) = 5 * 2^x, what is the value of f(x)?

• 0

• 1

• 5

• 10

What is the y-value of f(x) when x = 0 in the original function f(x) = 5 * 2^x?

• 10

• 5

• 1

• 0

In the modified function f(x + 5), what x value corresponds to f(0) in the original function?

• f(10)

• f(0)

• f(5)

• f(6)

How does the graph of f(x + 5) compare to the original graph in terms of speed of increase?

• It decreases.

• It increases faster.

• It increases slower.

• The rate of increase is unchanged.

What is the effect of adding a constant to the x value in a function?

• It shifts the graph upwards.

• It shifts the graph downwards.

• It shifts the graph to the left.

• It shifts the graph to the right.

In the context of graph shifts, what does adding a constant to x in f(x) signify?

• A change in slope.

• A horizontal shift.

• A change in y-intercept.

• A vertical shift.

What happens to the graph of f(x) when a positive constant is added to x?

• It moves downwards.

• It moves upwards.

• It shifts to the left.

• It shifts to the right.

How does the graph of f(x + 5) differ from f(x) in terms of x-values?

• The x-values are reversed.

• Larger x-values are reached sooner.

• The x-values remain the same.

• Smaller x-values are reached sooner.