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United StatesMaths

Functions

6 dot points across 6 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you interpret exponential growth and decay, distinguish them from linear change, and read logarithms on the ACT?

Interpret exponential functions for growth and decay, distinguish exponential from linear change, work with compound growth, and read basic logarithms as inverse exponents (Functions).
An ACT Functions answer on exponential growth and decay: the form a times b to the x, the meaning of the initial value and growth factor, exponential versus linear change, compound growth, and reading logarithms as inverse exponents, with worked ACT-style questions.
11 min answer →

How do you read function notation, evaluate functions, and find domain and range on the ACT?

Read and use function notation, evaluate functions including composition, and identify domain and range from rules and graphs (Functions).
An ACT Functions answer on function notation: evaluating a function at a value, composing functions, finding domain and range, and reading function values from a graph or table, with worked ACT-style questions and common traps.
10 min answer →

How do you interpret linear functions, slope as a rate of change, and build a linear model on the ACT?

Interpret a linear function's slope as a rate of change and its intercept as a starting value, build linear models, and read slope from points, tables and graphs (Functions).
An ACT Functions answer on linear functions: slope as a rate of change, the y-intercept as a starting value, building a linear model from a rate and an initial amount, and reading slope from points, tables and graphs, with worked ACT-style questions.
10 min answer →

How do you read a quadratic function's graph, including its vertex, intercepts and axis of symmetry, on the ACT?

Read a parabola from the three forms of a quadratic, find the vertex, axis of symmetry, intercepts and direction of opening, and identify maximum or minimum values (Functions).
An ACT Functions answer on quadratic functions and their parabola graphs: the standard, factored and vertex forms, finding the vertex and axis of symmetry, the intercepts, direction of opening, and maximum or minimum value, with worked ACT-style questions.
11 min answer →

How do you work with arithmetic and geometric sequences on the ACT, including finding a term and a sum?

Identify arithmetic and geometric sequences, find a specified term using the explicit rule, and compute simple sums (Functions).
An ACT Functions answer on sequences and series: recognising arithmetic (constant difference) and geometric (constant ratio) sequences, finding the nth term with the explicit formula, and computing simple sums, with worked ACT-style questions and common traps.
10 min answer →

How do shifts, reflections and stretches transform the graph of a function on the ACT?

Apply vertical and horizontal shifts, reflections and stretches to the graph of a function, and read a transformed function's equation from its parent (Functions).
An ACT Functions answer on transformations: vertical and horizontal shifts, reflections across the axes, and vertical stretches and compressions, how each changes the equation, and reading a transformed graph, with worked ACT-style questions.
10 min answer →