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MassachusettsMaths

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 compare functions given in different forms, and how do you build a function from a description or table?

Compare properties of two functions represented in different ways (graph, table, equation, words), and build a function (linear or exponential) to model a relationship from a description or data.
A Grade 10 Math MCAS answer on comparing functions across representations (graph, table, equation, words) and building a linear or exponential model from a description or data, including the average rate of change.
9 min answer →

How do exponential functions model growth and decay, and how do they differ from linear functions?

Write and interpret exponential functions for growth and decay, identify the initial value and growth factor, and contrast exponential change (constant ratio) with linear change (constant difference).
A Grade 10 Math MCAS answer on exponential functions: modeling growth and decay, reading the initial value and growth or decay factor, and distinguishing exponential change (constant ratio) from linear change (constant difference).
9 min answer →

What is function notation, and how do you read the key features of a function from its graph or table?

Use and interpret function notation, evaluate functions, identify domain and range, and read key features (intercepts, intervals of increase and decrease, maximum and minimum) from a graph or table.
A Grade 10 Math MCAS answer on function notation and evaluation, domain and range, and reading key features (intercepts, increasing and decreasing intervals, maxima and minima) from a graph or table.
9 min answer →

How do you find the slope and equation of a line, and what does the rate of change mean in context?

Find the slope of a line from two points, write linear equations in slope-intercept and point-slope form, and interpret slope as a constant rate of change in context.
A Grade 10 Math MCAS answer on linear functions: computing slope from two points, writing equations in slope-intercept and point-slope form, parallel and perpendicular slopes, and interpreting slope as a constant rate of change.
9 min answer →

How do you read the vertex, axis of symmetry, and intercepts of a parabola, and what do the three forms tell you?

Graph quadratic functions, find the vertex and axis of symmetry, identify zeros and the y-intercept, and connect standard, factored, and vertex forms to the parabola's features.
A Grade 10 Math MCAS answer on quadratic functions: the parabola's vertex and axis of symmetry, zeros and y-intercept, the direction of opening, and how standard, factored, and vertex forms reveal different features.
10 min answer →

How do changes to a function's equation shift, stretch, or reflect its graph?

Describe and apply transformations of functions: vertical and horizontal shifts, reflections, and vertical stretches or compressions, and connect a change in the equation to the change in the graph.
A Grade 10 Math MCAS answer on function transformations: vertical and horizontal shifts, reflections across the axes, and vertical stretches and compressions, and how each change in the equation moves the graph.
9 min answer →