Name _____________________________
Algebra I
Unit 2 Day 3 Translations and Intercepts
Date ____________
The four functions given below are written in function notation .
f  x   2x
x
f  x   2x  2
f  x
x
f  x
f  x   2x  3
x
f  x
f  x   2x  4
x
–3
–4
–1
–5
–1
–3
0
–3
0
–1
1
–2
2
0
3
0
3
2
4
1
y-intercept: ______
y-intercept:_______
y-intercept:_______
f  x
y-intercept:_______
How does the function rule define the y-intercept?
f  x   2x
Number after “ x ” term:___________
y-intercept: __________
f  x   2x  2
Number after “ x ” term:___________
y-intercept: __________
f  x   2x  3
Number after “ x ” term:___________
y-intercept: __________
f  x   2x  4
Number after “ x ” term:___________
y-intercept: __________
Do you see a pattern?
Let’s apply the rules we just learned to other functions that are not linear.
Below are graphs of functions
f  x  , g  x  and h  x  .
Use the same y-intercept rule you just learned to draw the graph requested in each case.
Draw f  x  1
Draw g  x   3
Draw h  x   4
g  x
f  x
h  x
So, for functions written in ____________________________, we can say:
 Adding a number to the function will:
 Subtracting a number from the function will:
Function Families are groups of functions that look the same – they just may not all be in
the same place on the graph. Each Function Family has a “Parent Function” which is
often centered around the origin or one key point. The rest of the “family” is made up of
functions that look basically the same as the parent function but may be in a different
location or have other slight differences to them (they might be upside down or extra
wide , etc.)
A) Linear Functions
Parent graph
Family Member A
Family Member B
B) Absolute Value Functions
Parent graph
Family Member A
Family Member B
C) Quadratic Functions
Parent graph
Family Member A
Family Member B
D) Exponential Functions
Parent graph
Family Member A
Family Member B