Exercise 46 Page 745

Horizontal translations occur when we add or subtract a value from the argument of a function. We can observe it more clearly in the table below.

Horizontal Translations
Translation left h units, h>0 y=f(x+ h)	Translation right h units, h>0 y=f(x- h)

In this case, we are asked to translate y=x-2 left by 34 unit. Therefore, we will need to add. y=f(x+ h) ⇔ y=(x+ h)-2 Now, we can substitute h= 34 and simplify the equation.

y=(x+h)-2

Substitute

h= 3/4

y=(x+ 3/4)-2

RemovePar

Remove parentheses

y=x+3/4-2

▼

Subtract fractions

NumberToFrac

a = 4* a/4

y=x+3/4-4(2)/4

Multiply

Multiply

y=x+3/4-8/4

SubFrac

Subtract fractions

y=x+(- 5/4)

AddNeg

a+(- b)=a-b

y=x-5/4

Finally, we have enough information to graph the transformed function.