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Unformatted text preview: 3.3 Graphing Linear Functions By the vertical line test, we know that all linear equations are
functions (except those whose graphs are vertical lines). The equation y = 2x + 3 can be written as f(x) : 2x + 3 Any linear equation (except vertical lines) can be written using
function notation: Solve equation for y
Replace y with f(x) Example:
Write the equation 2x + 3y : 6 using function notation.
: ~21 +03
IE} “'23” "a?
\l : “2% X + 1 Another way to graph a linear equation or function is to find
and plot the x— and y— intercepts. To find an x—intercept, let y = O or f(x) = O and solve for x. To find a y—intercept, let x = O and solve for y. Example:
Graph 2x + 3y = 6 by plotting intercepts. ‘ X’Jmlii Y~lh+1 I \ 2x4’5(03”U’
I’?’ ..- Z. x13 farti- When a linear funcTion is wri’rien in The form y = mx + b
or f(x) = mx + b, The y—in’rercepT is (O, b)! Example:
Wha’r are The x— and y—in’rercepis of f(x) = 2x —- 4?
‘--..Ii' ~ ‘m‘l 'ZX * Ll =0
(inqyl 2x : q II
- X : Z (210)". Graphing Veriical and Horizontal Lines The graph of x = c is a ver’rical line wiTh x-inTercepl' (c, O) The graph of y = c is a horizom‘al line with y-inTer-cep’r (0, c) Examples: \
Graph x = -2 I
Graph y : 4 Homework: p. 162 #1-33 add (Bonus: 73) ...
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- Spring '08