Exponential Functions and Transformations

The video tutorial introduces exponential growth, explaining the basic formula y = b^x, where b > 1 and b ≠ 0. It discusses the conditions for exponential growth, emphasizing that the graph increases when b is greater than one. The tutorial covers graphing exponential functions, highlighting the importance of the y-intercept at (0,1). It also explores transformations of exponential graphs, including shifting, reflecting, and stretching. The video concludes with a summary of the basics of exponential growth.

What is the basic form of an exponential growth equation?

• y = b^x

• y = ax^2 + bx + c

• y = a/x

• y = mx + c

For exponential growth, what must be true about the base 'b'?

• b must be equal to 1

• b must be equal to 0

• b must be less than 0

• b must be greater than 1

What is the y-intercept of the parent exponential growth graph?

• (0, 1)

• (1, 0)

• (0, 0)

• (1, 1)

How does the graph of an exponential function behave as it moves to the right?

• It oscillates

• It decreases

• It remains constant

• It increases

What transformation is applied when 'h' is changed in the equation y = a * b^(x-h) + k?

• Vertical shift

• Horizontal shift

• Vertical stretch

• Reflection

In the equation y = a * b^(x-h) + k, what does 'k' represent?

• Reflection

• Vertical shift

• Horizontal shift

• Horizontal stretch

What effect does a negative 'a' have on the graph of an exponential function?

• It shifts the graph up

• It compresses the graph vertically

• It stretches the graph horizontally

• It reflects the graph over the x-axis

Which parameter affects the vertical stretch or compression of an exponential graph?

• a

• k

• b

• h

What happens to the graph of y = a * b^(x-h) + k if 'b' is less than 1?

• The graph represents exponential decay

• The graph becomes a straight line

• The graph remains unchanged

• The graph represents exponential growth

Which transformation is not possible with the equation y = a * b^(x-h) + k?

• Vertical shift

• Horizontal shift

• Reflection over the y-axis

• Reflection over the x-axis