2.4 Exponential function manipulation
Write the product property for exponents and briefly explain its implication on the graphical transformation of an exponential function.
Write the power property for exponents and briefly explain its implication on the graphical transformation of an exponential function.
What is the value of an exponential expression when the exponent is negative? Write the negative exponent property.
What is the value of an exponential unit fraction expression, such as b^{\frac{1}{k}} where k is a natural number?
Given the function f(x) = b^{x+k}, write an equivalent function using the product property for exponents.
Given the function f(x) = 2^{x - 3}:
Using the product property of exponents, rewrite the function in the form f(x) = ab^x.
What will be the values of a and b?
Given the function f(x) = 3^{2x}:
Using the power property of exponents, rewrite the function in the form f(x) = a^x.
What is the value of a?
The function f(x) = (4^{x})^2 represents the profit of a company.
Using the power property for exponents, rewrite the function in the form f(x) = a^x.
What is the new base a?
Given the function f(x) = 10^{x+5}:
Using the product property for exponents, rewrite the function in the form f(x) = ab^x.
What are the values of a and b?
Simplify the expression (3^{x})^{-4} using the power property for exponents.
Simplify the expression 5^{-2} using the negative exponent property.
Simplify the following expressions involving an exponential unit fraction:
9^{\frac{1}{2}}
4^{\frac{1}{2}}
16^{\frac{1}{2}}
25^{\frac{1}{2}}
Consider the function f(x) = 3^{2x+1}.
Rewrite the function using the product and power properties of exponents.
How does this transformation affect the graph of the function?
Given the function f(x) = 2^{x - 3}, explain how the graph of this function would change if we were to rewrite it using the product property for exponents. Consider shifts, stretches, and reflections in your explanation.
The function g(x) = (5^x)^{-2} models the decay of a certain substance. Rewrite this function using the power property for exponents and interpret the meaning of the new base in the context of the substance's decay.