Domain & Range
Find the domain of the discrete relation:
{(-4,2), (0,5), (2,8), (5,2)}
{-4, 0, 2, 5}
What graphical test is used to determine if a graph represents a function?
The Vertical Line Test
Write the algebraic rule of the Linear parent function
f(x)=x
Describe the transformation:
f(x)=|x|-4
Down 4 units
Write an absolute value equation shifted up 4 units
f(x)=|x|+4
Find the range of the discrete relation:
{(-4,2), (0,5), (2,8), (5,2)}
{2, 5, 8}
Is this relation a function?
{(1,2),(3,4),(1,5),(6,7)}
No
Write the algebraic rule and describe the shape of the absolute value parent function
f(x)=|x|
"V" shaped centered at the origin (0,0)
Describe the shift:
f(x)=|x-1|
Right 1 unit
Write an absolute value equation shifted right 3 units and up 2 units
f(x)=|x-3|+2
What is the domain of any standard linear parent function y=x
(-infty,infty)
Does a vertical line x=3 represent a function? Explain
No, fails vertical line test
Write the algebraic rule and describe the shape of the Quadratic parent function
f(x)=x^2
"U" shaped; Parabola
Describe all transformations you see:
f(x)=-|x|+5
Reflect over x-axis and translated up 5 units
Write an absolute value equation reflected over the x-axis and shifted left 9 units
f(x)=-|x+9|
State the domain and range of f(x)=|x|-4
D: (-infty,infty)
R: [-4,infty)
Does a horizontal line y=-2 represent a function? Explain
Yes, it passes the vertical line test
Write the algebraic rule and domain of the Square Root parent function
f(x)=sqrt(x)
Describe the transformations you see:
f(x)=1/4|x-5|+1
1) Vertical shrink by 1/4
2) Right 5 units
3) Up 1 unit
Write an absolute value equation with a vertical stretch of 3, translated right 2 units, and down 7 units
f(x)=3|x-2|-7
A quadratic function has a maximum vertex at (2,-5). State its domain and range.
D: (-infty,infty)
R: (-infty,-5]
Evaluate f(x)=-x^2-3x+5 for f(2)
f(2)=-5
Evaluate f(x)=-4|x-1|+3 for f(-3)
f(-3)=-13
Describe all transformations:
f(x)=-4/3|x+5|+12
1) Reflection over the x-axis
2) Vertical stretch by a factor of 4/3
3) Shifted left 5 units
4) Shifted up 12 Units
Write the equation of a graph that is vertically shrunk by a factor of 2/5, shifted to the left 11 units, and shifted down 7 units
f(x)=2/5|x+11|-7