Exploring Adding and Subtracting Rational Expressions

The video tutorial covers transformations of exponential functions, including horizontal and vertical shifts, reflections, and stretches/compressions. It explains how to identify parent functions and apply transformations to graph them. The tutorial includes practice problems to reinforce understanding of these concepts.

What happens to the graph of an exponential function when a positive constant is added to the exponent?

• The graph shifts to the right.

• The graph shifts to the left.

• The graph shifts upward.

• The graph shifts downward.

If the base of an exponential function is multiplied by a constant greater than 1, what transformation occurs?

• Vertical compression

• Vertical shift

• Vertical stretch

• Horizontal shift

For the function f(x) = 3^(x) + 5, what is the transformation applied to the parent function?

• Shift left 5

• Shift right 5

• Shift up 5

• Shift down 5

What is the parent function of f(x) = 2 * (1/4)^(x-1)?

• f(x) = (1/2)^(x)

• f(x) = 4^(x)

• f(x) = (1/4)^(x)

• f(x) = 2^(x)

In the function f(x) = - (4/3)^(x+2) + 7, what does the negative sign indicate?

• Vertical compression

• Reflection across the x-axis

• Reflection across the y-axis

• Vertical stretch

What is the effect of a vertical compression on the graph of an exponential function?

• The graph shifts downward.

• The graph shifts upward.

• The graph becomes narrower.

• The graph becomes wider.

For the function f(x) = 2^(x+5), what is the horizontal shift applied to the parent function?

• Shift left 5

• Shift right 5

• Shift up 5

• Shift down 5

What is the new range of the function f(x) = 3^(x) + 1 after a vertical shift up by 1?

• y < 0

• y > 0

• y < 1

• y > 1

In the function f(x) = -2 * 4^(x-2), what is the effect of the -2 coefficient?

• Vertical stretch and reflection across the x-axis

• Vertical compression and reflection across the y-axis

• Horizontal stretch and reflection across the x-axis

• Horizontal compression and reflection across the y-axis

For the function f(x) = (3/2)^(x-4) - 5, what is the vertical shift applied to the parent function?

• Shift up 5

• Shift down 5

• Shift down 4

• Shift up 4