UNIT 1

CORE MATH 1-1

Example 1: Translate the point (4,-3) 6 units to the right and up 2 units.

6 units right, add to the x coordinate
2 units up, add to the y coordinate Therefore new point is (10,-1)

CORE MATH 1-2

PARENT FUNCTIONS

TRANSLATIONS OF FUNCTIONS

EXAMPLES

Explore the graph f(x) = (x-2)^3

1) What is the parent function? f(x) = x^3

2.) Predict what the how the function will translate?

the new function will shift right 2 units

Identify the translations

1) f(x) = (x-3)^2 +5

the graph shifts right 3 and up 5 units

2) g(x) = -(x+2)^3

the graph reflects across the x-axis and shifts left 2 units

CORE MATH 1-3

TRANSFORMING LINEAR FUNCTIONS

Linear function f is transformed to produce g. Write g(x) in terms of f(x).

1.) f(x) = 7x - 3 is translated 2 units down.

g(x) = 7x - 2 - 3 then simplify to g(x) = 7x - 5

2.) f(x) = 2x +3 is translated 5 units right.

g(x)= 2(x - 5) + 3 then simplify to g(x)= 2x - 10 +3 = g(x)=2x - 7

3.) f(x) = 5x - 3 is reflected across the x-axis

distribute f(x) by -1 g(x) = -5x + 3

4.) f(x) = 2x + 4 is reflected across the y-axis

only multiply the x values by -1 g(x) = -2x + 4