Function Tables 02/12/12 lntaylor ©

Table of Contents Learning Objectives Linear Equations Build a Function Table Build a T Chart Reading a Function Table Graphing from a Function Table Quadratic Equations Build a Function Table 02/12/12 lntaylor ©

Learning Objectives TOC 02/12/12 lntaylor ©

Learning Objectives LO 1 LO 2 Understand what a Function Table represents Perform basic operations with Function Tables LO 3Build ANY Equations from a Function Table TOC 02/12/12 lntaylor ©

Definitions Definition 1 A Function Table is a way of expressing a relationship between x and y values TOC Definition 2 A T Chart is a Function Table in a different format Definition 3 A Function states that for every x there is one particular y Definition 4f(x) is another way of saying “function” or “y = “ 02/12/12 lntaylor ©

Previous knowledge PK 1Basic Operations and Properties TOC 02/12/12 lntaylor ©

Rule 1 Rule 2 Plug in x = 0 and find y Go up and down the same amount for each additional x value Rule 3 Always check your work Basic Rules of Function Tables TOC 02/12/12 lntaylor ©

Build a Function Table TOC 02/12/12 lntaylor ©

Build a Function Table Build a Function Table for f(x) = 2x + 1 –You are given certain information in a function f(x) Given a slope (m) which is the number in front of the x Given a y intercept (yi or b) which is the number after the x Start with x = 0 and plug it into the equation; find y Go up or down the same amount for the next x’s TOC 02/12/12 lntaylor ©

f(x) = 2x + 1 Step 1 – Construct Table Build 3 column Table Build Headings Step 2 – Choosing x values Start with x = 0 Plug 0 into equation Solve for y Build x column Build middle column Build y column Check your work! Note that every x has one y x and y together are called ordered pairs (coordinates and a single point on a graph) TOC 2x + 1 xf(x) or y 02(0) (-3) + 1 2(-2) + 1 2(-1) + 1 2(0) + 1 2(1) + 1 2(2) + 1 2(3) /12/12 lntaylor ©

Now you try! y = 3x - 5 TOC 02/12/12 lntaylor ©

f(x) = 3x - 5 Step 1 – Construct Table Build 3 column Table Build Headings Step 2 – Choosing x values Start with x = 0 Plug 0 into equation Solve for y Build x column Build middle column Build y column Check your work! Note that every x has one y x and y together are called ordered pairs (coordinates and a single point on a graph) TOC 3x - 5 xf(x) or y 03(0) (-3) - 5 3(-2) - 5 3(-1) - 5 3(0) - 5 3(1) - 5 3(2) - 5 3(3) /12/12 lntaylor ©

Now you try! y = - 3x - 5 TOC 02/12/12 lntaylor ©

f(x) = -3x - 5 Step 1 – Construct Table Build 3 column Table Build Headings Step 2 – Choosing x values Start with x = 0 Plug 0 into equation Solve for y Build x column Build middle column Build y column What is different between the last two equations? y values are reversed! Why? The slope sign changed! TOC -3x - 5 xf(x) or y 03(0) (-3) (-2) (-1) (0) (1) (2) (3) /12/12 lntaylor ©

Build a T Chart TOC 02/12/12 lntaylor ©

Build a T Chart Build a T Chart for f(x) = 2x + 1 –You are given certain information in a function f(x) Given a slope (m) which is the number in front of the x Given a y intercept (yi or b) which is the number after the x Start with x = 0 and plug it into the equation; find y Go up or down the same amount for the next x’s TOC 02/12/12 lntaylor ©

f(x) = 2x + 1 Step 1 – Construct T Chart Build 2 column Table Build Heading Step 2 – Choosing x values Start with x = 0 Plug 0 into equation Solve for y Build x column Build y column Check your work! Note that every x has one y x and y together are called ordered pairs (coordinates and a single point on a graph) TOC 2x x, y -3, -5 -2, -3 -1, -1 0, 1 1, 3 2, 5 3, 7 02/12/12 lntaylor ©

Now you try! y = - x - 5 TOC 02/12/12 lntaylor ©

f(x) = - x - 5 Step 1 – Construct T Chart Build 2 column Table Build Heading Step 2 – Choosing x values Start with x = 0 Plug 0 into equation Solve for y Build x column Build y column Check your work! Did you? Note that every x has one y x and y together are called ordered pairs (coordinates and a single point on a graph) TOC - x x, y -3, -2 -2, -3 -1, -4 0, -5 1, -6 2, -7 3, -8 02/12/12 lntaylor ©

Reading a Function Table (T Chart) TOC 02/12/12 lntaylor ©

Reading a Function Table or a T Chart Read a T Chart for f(x) –You are given certain information in a function f(x) Given a Δy – how much each y value changes Given a Δx – how much each x value changes The slope m is Δy/ Δx Given a y intercept (yi or b) which is where x = 0 TOC 02/12/12 lntaylor ©

What is f(x)? Step 1 – Find Δ y subtract each y value from the one above it Is it consistent? Step 2 - Find Δ x Subtract each x value from the one above it Is it consistent? Step 3 – find m and b Slope (m) = Δ y/ Δ x B or yi intercept where x = 0 Step 4 – write f(x) TOC – 7 = – 2 3 – 5 = – 2 1 – 3 = – 2 – 1 – 1 = – 2 – 3 – – 1 = – 2 – 5 – – 3 = – 2 yes – 2 – – 3 = 1 – 1 – – 2 = 1 0 – – 1 = 1 1 – 0 = 1 2 – 1 = 1 3 – 2 = 1 yes Δ y = – 2x Δ x = 1 f(x) = -2x /12/12 lntaylor ©

Now you try! TOC 02/12/12 lntaylor ©

What is f(x)? Step 1 – Find Δ y subtract each y value from the one above it Is it consistent? Step 2 - Find Δ x Subtract each x value from the one above it Is it consistent? Step 3 – find m and b Slope (m) = Δ y/ Δ x B or yi intercept where x = 0 Step 4 – write f(x) TOC – 2 – – 4 = 2 0 – – 2 = 2 2 – 0 = 2 4 – 2 = 2 6 – 4 = 2 8 – 6 = 2 yes – 2 – – 3 = 1 – 1 – – 2 = 1 0 – – 1 = 1 1 – 0 = 1 2 – 1 = 1 3 – 2 = 1 yes Δ y = 2x Δ x = 1 f(x) = 2x /12/12 lntaylor ©

Now you try! TOC 02/12/12 lntaylor ©

What is f(x)? Step 1 – Find Δ y subtract each y value from the one above it Is it consistent? Step 2 - Find Δ x Subtract each x value from the one above it Is it consistent? Step 3 – find m and b Slope (m) = Δ y/ Δ x B or yi intercept where x = 0 Step 4 – write f(x) TOC – 5 = – 2 1 – 3 = – 2 – 1 – 1 = – 2 – 3 – – 1 = – 2 – 5 – – 3 = – 2 – 7 – – 5 = – 2 yes – 4 – – 6 = 2 – 2 – – 4 = 2 0 – – 2 = 2 2 – 0 = 2 4 – 2 = 2 6 – 4 = 2 yes Δ y = - 2x Δ x = 2 f(x) = – x – 1 – 1 02/12/12 lntaylor ©

Graphing from a Function Table TOC 02/12/12 lntaylor ©

Graph f(x) TOC xy Step 1 Find x = 0 Locate coordinate on graph Find 2 nd point Find 3 rd point Draw line Label Line y = - x /12/12 lntaylor ©

Now you try! TOC 02/12/12 lntaylor ©

Graph f(x) TOC xy Step 1 Find x = 0 Locate coordinate on graph Find 2 nd point Find 3 rd point Draw line Label Line y = 2x 02/12/12 lntaylor ©

Now you try! TOC 02/12/12 lntaylor ©

Graph f(x) TOC xy Step 1 Find x = 0 Locate coordinate on graph Find 2 nd point Find 3 rd point Draw line Label Line y = - ¾ x 02/12/12 lntaylor ©

Quadratics Build a Function Table TOC 02/12/12 lntaylor ©

Quadratic Equations Quadratic Equations f(x) = ax² + bx + c –You are given certain information in a function f(x) Width of the curve is determined by (a) Symmetry is determined by (the opposite of b/2a) Y intercept of the curve is determined by (c) Remember all function tables are the same regardless of the equation Go up or down the same amount and look for consistency TOC 02/12/12 lntaylor ©

f(x) = x² - 5x - 6 Step 1 – Construct Table Build 3 column Table Build Headings Step 2 – Choosing x values Start with x = 0 Plug 0 into equation Solve for y Build x column Build middle column Build y column Check your work! Note that every x has one y x and y together are called ordered pairs (coordinates and a single point on a graph) TOC x² - 5x - 6 xf(x) or y 00² -5(0) (-3)² -5(-3) - 6 (-2)² -5(-2) - 6 (-1)² -5(-1) - 6 (0)² -5(0) - 6 (1)² -5(1) - 6 (2)² -5(2) - 6 (3)² -5(3) /12/12 lntaylor ©

Now you try! f(x) = x² + 2x + 1 TOC 02/12/12 lntaylor ©

f(x) = x² + 2x + 1 Step 1 – Construct Table Build 3 column Table Build Headings Step 2 – Choosing x values Start with x = 0 Plug 0 into equation Solve for y Build x column Build middle column Build y column Check your work! Note that every x has one y x and y together are called ordered pairs (coordinates and a single point on a graph) TOC x² + 2x + 1 xf(x) or y 00² + 2(0) (-3)² + 2(-3) + 1 (-2)² + 2(-2) + 1 (-1)² + 2(-1) + 1 (0)² + 2(0) + 1 (1)² + 2(1) + 1 (2)² + 2(2) + 1 (3)² + 2(3) /12/12 lntaylor ©

Now you try! f(x) = x² - 4 TOC 02/12/12 lntaylor ©

f(x) = x² - 4 Step 1 – Construct Table Build 3 column Table Build Headings Step 2 – Choosing x values Start with x = 0 Plug 0 into equation Solve for y Build x column Build middle column Build y column Check your work! Note that every x has one y x and y together are called ordered pairs (coordinates and a single point on a graph) TOC x² - 4 xf(x) or y 00² (-3)² - 4 (-2)² - 4 (-1)² - 4 (0)² - 4 (1)² - 4 (2)² - 4 (3)² /12/12 lntaylor ©