Understanding Exponential Functions

The video tutorial introduces exponential functions, defining them as functions of the form y = a*b^x, where a and b are constants. It explains the conditions for a and b, and demonstrates graphing exponential functions using f(x) = 2^x and g(x) = 5*(1/2)^x. Key features such as domain, range, intercepts, and asymptotes are discussed, along with the end behavior of these functions as x approaches positive and negative infinity.

What is the general form of an exponential function?

• y = a - b^x

• y = a / b^x

• y = a * b^x

• y = a + b^x

Why can't the constant 'a' be zero in an exponential function?

• It would result in a linear function.

• It would make the function undefined.

• It would make the function non-continuous.

• It would result in a horizontal line.

What is the y-value when x = 0 for the function f(x) = 2^x?

• 0

• 1

• 2

• 4

What is the domain of the function f(x) = 2^x?

• x = 0

• x > 0

• x < 0

• All real numbers

What is the range of the function f(x) = 2^x?

• All real numbers

• y = 0

• y < 0

• y > 0

What happens to the y-values of f(x) = 2^x as x approaches negative infinity?

• They become negative.

• They remain constant.

• They approach zero.

• They approach positive infinity.

What is the effect of having a base b between 0 and 1 in an exponential function?

• The function remains constant.

• The function decreases.

• The function increases.

• The function oscillates.

What is the y-intercept of the function g(x) = 5 * (1/2)^x?

• (0, 1)

• (0, 5)

• (0, 2)

• (0, 0.5)

What is the asymptote of the function g(x) = 5 * (1/2)^x?

• y = 0

• y = -1

• y = 1

• y = 5

As x approaches positive infinity, what happens to g(x) = 5 * (1/2)^x?

• It approaches zero.

• It becomes negative.

• It approaches positive infinity.

• It remains constant.