Aim for FivePrecalculus

Function concepts

An exponential function and a log-like table

  • Unit 2
  • 6 points
  • About 18 minutes

You can use a calculator on this question, just like on exam day.

You work with functions given as a table, a graph described in words, or an equation: composition, inverses, zeros, end behavior and asymptotes, and picking the function type that fits a table. You'll use a graphing calculator. On the exam: Question 1 of 4. Part A of the free-response section: 2 questions in 35 minutes, graphing calculator required.

The question and its sources

A graphing calculator is required for this question. Make sure it is in radian mode. Unless otherwise specified, decimal approximations should be accurate to three places after the decimal point; avoid rounding intermediate values. Unless otherwise specified, the domain of a function f is the set of all real numbers x for which f(x) is a real number. Show the work that leads to your answers where the question asks for it.

Values of g

x124816
g(x)5791113

Source: Hypothetical function values

The functions f and g

The function g is increasing and is defined for x > 0. The table gives values of g(x) at selected values of x.

The function f is given by f(x) = 3 · 2^(0.5x) − 5.

Source: Hypothetical functions

Suggested time: 18 minutes

Your answers are saved in this browser as you type.

Part (a)

2 points

(i) The function h is defined by h(x) = (f ∘ g)(x) = f(g(x)). Find the value of h(2) as a decimal approximation, or indicate that it is not defined. Show the work that leads to your answer. (ii) Find the value of g⁻¹(11), or indicate that it is not defined.

0 / 2,500 characters

Part (b)

2 points

(i) Find all values of x, as decimal approximations, for which f(x) = 0, or indicate that there are no such values. (ii) Determine the end behavior of f as x decreases without bound. Express your answer using the mathematical notation of a limit.

0 / 2,500 characters

Part (c)

2 points

(i) Based on the table, which of the following function types best models g: linear, quadratic, exponential, or logarithmic? (ii) Give a reason for your answer to part (c)(i) based on the relationship between the change in the output values of g and the change in the input values of g. Refer to values in the table in your reasoning.

0 / 2,500 characters

Checking scoring…

Scoring it yourself shows you the rubric, examples and a model answer. Try writing your answer first.