Graph Transformations
Describe how the graph is moving:
y= |x|+3
up 3 units
Does the relation define a function?
{(5,3),(2,3),(3,4)}
Yes it is a function. Each x-value is different
Find the slope of the line containing (-5,3) and (8,4)
m= 1/13
Give the shape, key point (vertex, starting point, center), Domain and Range and also the Transformations of Function equation of:
y=|x|
V-shaped
Vertex (h,k)
Domain (-∞,∞)
Range [0,∞)
f(x)=a|x-h|+k
(1,2) (3,4)
1
Describe how the graph is moving:
y= |x+5|
right 5 units
Does the relation define a function? Explain
{(5,2),(4,3),(3,4) (5,0)}
No it is not a funtion the 5 is repeating
Find the slope of the line: Horizontal, through (6,2)
m=0
*Horizontal line always 0 slope*
What type of function is this?
y=x2
And this is traditionally
Quadratic
(8,5) (4,3)
-1/2
Describe how the graph is moving:
y= |x-3|-1
down 1 unit and to the left 3 units
let h(x)=x2+6x+2; Find and simplify h(3)
h(3)=29
Write an equation in slope-intercept form.
Through (6,8) and parallel to y=-8
*might be helpful to use the Point-slope formula*
Slope-intercept form: y=8
What type of function is this?
y=x3
Cubic
(12,18) (24,32)
7/6
Describe how the graph is moving:
y= -|x|-6
down 6 units and reflected over the x- axis
X Y
1 5
2 5
3 5
4 5
Yes it is a function
Write an equation in slope-intercept form:
Through (-1,5) and parallel to x+2y=5
*might be helpful to put equation in slope-int form first then use the point-slope formula*
slope-intercept form: y=(-1/2)x+9/2
What type of function is this? Describe the graph
y=√x
Square root function...it is a swoosh line
(6.5,7.2) (8.5, 9.2)
1
Describe how the graph is moving:
y= 3|x|
Vertical stretch
Let f(x)={(6,3),(-1,6),(-3,7)}; Find f(6)
f(6)=3
Write an equation in slope-intercept form:
Through (1,6) and perpendicular to 2x+5y=1
slope intercept form: y= (5/2)x+7/2
Is this a function? Why or Why not?
x=y2
Not a function because it Does NOT pass the vertical line test.
(-3,-5) (8,7)
12/11