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OhioMaths

Functions

7 dot points across 7 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

What is the average rate of change of a function over an interval, how do you compute it from a table or graph, and how does it relate to slope?

Calculate and interpret the average rate of change of a function over a specified interval from an equation, table, or graph, and connect it to slope (Ohio F-IF.6).
An Ohio Algebra I answer on average rate of change (F-IF.6): the change-in-output over change-in-input formula, computing it from tables and graphs, its meaning as slope, and how it differs for linear versus nonlinear functions.
11 min answer →

How do you build a function that models a situation, write a linear function from a description or two points, and use it to make predictions?

Build a function that models a relationship, write a linear function from a context, table, or two points, and interpret its parameters in context (Ohio F-BF.1, F-LE.2, F-IF.7).
An Ohio Algebra I answer on building functions (F-BF.1, F-LE.2): writing a linear function from a verbal description, a table, or two points, interpreting the slope and intercept as rate and starting value, and using the function to predict.
12 min answer →

How do you tell whether a situation is linear, quadratic, or exponential from a table, graph, or description, and which one grows fastest?

Distinguish linear, quadratic, and exponential functions from tables, graphs, and contexts using constant differences and ratios, and compare their long-run growth (Ohio F-LE.1, F-LE.3, F-IF.4).
An Ohio Algebra I answer on comparing function families (F-LE.1, F-LE.3): constant first differences for linear, constant second differences for quadratic, constant ratios for exponential, and why exponential growth eventually overtakes the others.
12 min answer →

What is an exponential function, how do the growth and decay models work, and how do you read the starting value and the rate?

Build and interpret exponential functions of the form f(x) = ab^x, including growth y = a(1+r)^t and decay y = a(1-r)^t, identifying the initial value and the rate (Ohio F-LE.1, F-LE.2, F-IF.8).
An Ohio Algebra I answer on exponential functions (F-LE.2, F-IF.8): the form f(x) = ab^x, the growth and decay percentage models, reading the initial value a and base b, and when growth beats linear change.
12 min answer →

What is a function, how do you read and evaluate function notation like f(x), and what do domain and range mean?

Use function notation to evaluate and interpret functions, decide whether a relation is a function, and identify domain and range from equations, tables, and graphs (Ohio F-IF.1, F-IF.2, F-IF.5).
An Ohio Algebra I answer on functions (F-IF.1, F-IF.2): the definition of a function, the vertical line test, evaluating f(x), solving f(x) = k, and reading domain and range from graphs and tables.
12 min answer →

How do you read the key features of a function's graph, intercepts, increasing and decreasing intervals, maximum and minimum, and positive and negative regions?

Identify and interpret key features of a graph, including intercepts, intervals of increase and decrease, relative maximum and minimum, and end behavior, in context (Ohio F-IF.4, F-IF.5).
An Ohio Algebra I answer on key features of graphs (F-IF.4): x- and y-intercepts, increasing and decreasing intervals, relative maxima and minima, positive and negative regions, and interpreting these in a real context.
12 min answer →

What is the difference between an arithmetic and a geometric sequence, and how do you find a term or write a rule for each?

Recognize, extend, and write rules for arithmetic and geometric sequences, using the explicit formulas, and treat sequences as functions of the term number (Ohio F-IF.3, F-BF.2, F-LE.2).
An Ohio Algebra I answer on sequences (F-BF.2, F-IF.3): telling arithmetic from geometric, the explicit formulas on the reference sheet, finding the nth term, and seeing sequences as functions whose domain is the whole numbers.
12 min answer →