In this worksheet, we will practice identifying, writing, evaluating, and analyzing exponential functions.
Q1:
What are the base and exponent of the function 𝑓(𝑥)=5?
Q2:
Write an exponential equation in the form 𝑦=𝑎(𝑏) for the numbers in the table.
Q3:
Given that 𝑓(𝑥)=6, determine the value of 𝑓(3).
Q4:
Suppose that 𝑓(𝑥)=0.3(4).
Evaluate 𝑓(0).
Evaluate 𝑓(2).
Evaluate 𝑓(0.5).
Evaluate 𝑓−12.
Q5:
Write an exponential equation in the form 𝑦=𝑏 for the numbers in the table.
Q6:
Given that 𝑓(𝑥)=3, find 𝑓(𝑥+9).
Q7:
Consider an exponential function with base 𝑎. For which values of 𝑎 is the function decreasing?
Q8:
Observe the given graph, and then answer the following questions.
Find the 𝑦-intercept in the shown graph.
As this graph represents an exponential function, every 𝑦-value is multiplied by 𝑏 when 𝑥 increases by Δ𝑥. Find 𝑏 for Δ𝑥=1.
Find the equation that describes the graph in the form 𝑦=𝑎𝑏.
Q9:
Given that 𝑓(𝑥)=8 and 𝑓(𝑥)=18, determine the value of 𝑓−𝑓(−4)𝑓−𝑓(−2).
Q10:
Given that 𝑓(𝑥)=4, determine the value of 𝑓(𝑥)𝑓(𝑥−1)−𝑓(𝑥−1)𝑓(𝑥).
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