WRITE AN EQUATION FOR A FUNCTION WITH THE GIVEN CHARACTERISTICS

Write an equation for the given characteristics.

Problem 1 :

Quadratic

up 2

right 3

Solution:

Parent function for quadratic function :

f(x) = x²

Up 2 units and right 3 units.

f(x) = (x - 3)² + 2

Problem 2 :

Cubic

reflected on the x-axis

down 4

Solution:

Parent function for quadratic function :

f(x) = x³

Reflection on x-axis, then put y = -y

f(x) = -x³

Down 4 units.

f(x) = -x³ - 4

Problem 3 :

Square Root

reflected on the y-axis

left 2

Solution:

f(x) = √x

Reflected on y-axis, then put x = -x

f(x) = √(-x)

Left 2 units.

f(x) = √(-x - (-2))

f(x) = √(-x + 2)

Problem 4 :

Absolute value

right 4

up 6

Solution:

Parent function for absolute value function :

f(x) = |x|

Right 4 units.

f(x) = |x - 4|

Up 6 units

f(x) = |x - 4| + 6

Problem 5 :

Reciprocal

reflected on the y-axis

up 4

right 2

Solution:

Problem 6 :

Quadratic

reflected on both axes

down 2

left 5

Solution:

Parent function for quadratic function :

f(x) = x²

Down 2 units :

f(x) = x² - 2

Left 5 units :

f(x) = (x - 5)² - 2

Problem 7 :

Cubic

down 3

right 7

Solution:

f(x) = x³

Down 3 units :

f(x) = x³ - 3

Right 7 units :

f(x) = (x - 7)³ - 3

Problem 8 :

Square Root

reflected on both axes

left 6

up 9

Solution:

f(x) = √x

Reflected on both axes means, reflection of x axis, then reflection on y-axis. Finally we will get the same.

Left 6 units :

f(x) = √(x - (-6))

f(x) = √(x + 6)

Up 9 units :

f(x) = √(x + 6) + 9