Function Transformation Math Example 3

Follow the full solution, then compare it with the other examples linked below.

easy

The graph of

y = f(x)

passes through

(1, 4)

. Where does the transformed graph

y = f(x+2) - 3

pass through?

1
Horizontal shift left $2$ : $x$ -coordinate becomes $1-2 = -1$ .
2
Vertical shift down $3$ : $y$ -coordinate becomes $4-3 = 1$ . New point: $(-1, 1)$ .

Answer

(-1,\, 1)

Adding a constant inside the function shifts the graph left (counterintuitive:

x+2

means every point moves to a smaller

x

-value). Subtracting outside shifts down. Together they map

(1,4)

(-1,1)

About Function Transformation

A function transformation shifts, stretches, compresses, or reflects the graph of a parent function by modifying its formula in a systematic way.

Describe all transformations applied to [formula] to obtain [formula].

Starting from [formula], apply the transformation [formula] step by step and identify the key point

Write the equation of the function obtained by reflecting [formula] over the [formula]-axis, compres