Question

graph 𝑓⁡(𝑥) =𝑥 +2 and its inverse

Answer 1

1) Find the inverse algebraically
- Start with y = x + 2.
- Swap x and y: x = y + 2.
- Solve for y: y = x − 2.
So f−1(x) = x − 2.

2) Key facts
- f(x) = x + 2 is a line with slope 1 and y-intercept 2.
- Points: (−2, 0), (0, 2), (1, 3).
- f−1(x) = x − 2 is a line with slope 1 and y-intercept −2.
- Points: (2, 0), (0, −2), (3, 1).
- Both have domain = range = (−∞, ∞).
- They are parallel (same slope) and symmetric with respect to the line y = x. Each point (a, a+2) on f corresponds to (a+2, a) on f−1.

3) How to draw them
- Draw coordinate axes.
- For f(x)=x+2, plot (0,2) and another point (1,3); draw the line through them.
- For f−1(x)=x−2, plot (0,−2) and (1,−1); draw that line.
- Also sketch y = x if you want to show the reflection symmetry.

If you’d like, I can generate a plotted image of these lines.