Unit 5, Lesson 6
Symmetry in Equations
Integrated Math 3
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Here is a graph of a function \(f\) for \(0 \leq x \leq 5\).
Function on coordinate plane, no grid. Horizontal x axis from negative 5 to 4 by 1's. Vertical y axis from negative 150 to 150 by 50's. Function passes through approximate values: 0 comma 0, 1 comma 5, 2 comma 12, 3 comma 25, 4 comma 50, 5 comma 125.
Here are the graphs of \(y = f(x)\) and \(y = f(x-1)\) for a function \(f\).
Which graph corresponds to each equation? Explain how you know.
Graph of 2 functions, no grid. Horizontal axis from negative 5 to 5, by 1's. Vertical axis from negative 100 to 100, by 25's. Green function on the left, starts at negative 5 comma 100, moves downwards until negative 1 point 5 comma 0, moves upwards until about 1 point 5 comma 12 point 5, then moves downwards passing thorugh 3 comma 0. Blue function on the right starts at negative 4 comma 100, moves downwards until negative 0 point 5 comma 0, moves upwards until 2 point 5 comma 12 point 5, then moves downwards passing through 4 comma 0.
Write an expression for two of the graphs in terms of \(f(x)\).
Graph of function f, a, b, c, and d. X axis from negative 6 to 8, by 2’s. Y axis from negative 6 to 8, by 2’s. From left to right, function f starts at the origin, moves upward and to the right to about 2 comma 4, downward to about 4 comma 0, and ends around 5 comma 1. Function a starts at around negative 6 comma 0, moves upward and to the right to about negative 4 comma 4, downward to about negative 2 comma 0, and ends around negative 1 comma 1. Function b starts at about 0 comma 2, moves upward and to the right to about 2 comma 6, downward to about 4 comma 2, and ends around 5 comma 3. Function c starts at about 4 comma 3, moves upward and to the right to about 6 comma 7, downward to about 8 comma 3, and ends around 9 comma 4. Function d starts at around 0 comma negative 5, moves upward and to the right to about 2 comma negative 1, downward to about 4 comma negative 5, and ends around 5 comma negative 4.
Here is a graph of the function \(f\) given by \(f(x) = x^3\).
Function on coordinate plane, no grid. Horizontal x axis from negative 5 to 5 by 1's. Vertical y axis from negative 150 to 150 by 50's. Function passes through negative 5 comma negative 125, negative 3 comma negative 9, negative 1 comma negative 1, 0 comma 0, 1 comma 9, 3 comma 9, 4 comma 64.