Absolute Value Equations
|2x-1| = 5
x = 3 or x = -2
5|y+3|<15
y>-6
y<0
Is this set a function?
{(10,2),(-10,2),(6,4),(5,3),(-6,7)}
Yes
x y
-2 3
1 4
2 7
Determine whether y varies directly with x. If so, find the constant of variation and write the function rule.
No
Y varies directly with x. Find the constant of variation. Then find the value of x when y = 5
y = 3 when x = -9
x = -15
|4-2y|+5 = 9
y=4 or y=0
|2t-3|≤5
t≤4
t≥-1
Is this set a function?
{(4,5),(1,5),(3,8),(4,6),(10,12)}
No
x y
2 6
3 9
8 24
Determine whether y varies directly with x. If so, find the constant of variation and write the function rule.
Yes
constant of variation: k=3
function rule: y=3x
x y
3 6
9 18
12 24
Determine whether y varies directly with x. If so, find the constant of variation and write the function rule.
Constant of Variation: k = 2
Function Rule: y=2x
|x+5|=3x-7
x=6
|4b|-3>9
b<-3
b>3
Find f(-0.5)
f(x) = -x+4
f(x) = 4.5
Y varies directly with x. Find the constant of variation. Then find the value of y when x = -0.3
y = 2 when x = -1/2
k=-4
y=1.2
What is the name of the test that states that if a vertical line passes through more than one point on the graph of a relation, then the relation is not a function?
Vertical Line Test
|4w+3|-2=5
w=1 or w=-5/2
|-2x+4|≥4
x≥4
x≤0
Find f(-2)
f(x) = -x+4
f(x)=6
Y varies directly with x. Find the constant of variation. Then find the value of y when x = -0.3
y = 7 when x = 2
k = 7/2
y = -1 and 1/20
Y varies directly with x. Find the constant of variation. Then find the value of x when y = 2
y = 5 when x = 8
3|2x+5|=9x-6
x=7
2|4x+1|-5≤1
x≤1/2
x≥-1
Find f(3)
f(x) = 3/8x-3
-1 and 7/8
Y varies directly with x. Find the constant of variation. Then find the value of y when x = -0.3
y = 4 when x = -3
k = -4/3
y = 0.4
f(12)
f(x) = 5x - 22
(12,38)