Exploring Exponential Functions in AP Precalculus

What is the general form of an exponential function?

• f(x) = a/b^x

• f(x) = ab^x

• f(x) = ax + b

• f(x) = a + bx

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

• It would make the function undefined.

• It would turn the function into a constant zero.

• It would invert the function.

• It would eliminate the variable x.

What condition on 'b' defines exponential growth?

• b = 0

• b < 0

• 0 < b < 1

• b > 1

What does exponential decay imply about the base 'b'?

• b = 1

• b > 1

• b < 0

• 0 < b < 1

How do you determine if an exponential function is increasing or decreasing?

• By the coefficient of x

• By the sign of the exponent

• By checking if 'a' is positive or negative

• By checking the value of 'b'

What does it mean if an exponential graph is concave up?

• It is linear.

• It is always decreasing.

• It has a point of inflection.

• It is always increasing.

What is the end behavior of an exponential function as x approaches positive infinity and the function is decaying?

• Approaches zero

• Remains constant

• Approaches negative infinity

• Approaches positive infinity

In an exponential function, if 'a' is negative, how does it affect the graph?

• Makes it concave up

• Makes it concave down

• Shifts it downwards

• Shifts it upwards

What is the behavior of an exponential function's graph as x approaches negative infinity and the function is growing?

• Approaches zero

• Becomes constant

• Approaches positive infinity

• Approaches negative infinity

If the output values of a function G(x) = f(x) + k are proportional, what can be inferred about f(x)?

• f(x) is a linear function

• f(x) is an exponential function

• f(x) is a quadratic function

• f(x) is a logarithmic function