Question

What transformation has changed the parent function f(x) = (.5)x to its new appearance shown in the graph below?

exponential graph passing through point 1, 2 and point 2, 1.

f(x) − 2
f(x + 2)
f(x − 2)
f(x) + 1

Answer 1

@triciaal

Answer 2

I'm not the best at math, but those transformations don't seem like they can do the trick.
\[f(x)=\frac12x\\
f(x)-2 = \frac12x-2\qquad\text{shift down 2}\\
f(x+2) = \frac12(x+2) = \frac12x+1\qquad\text{shift up 1}\\
f(x-2) = \frac12(x-2) = \frac12x-1\qquad\text{shift down 1}\\
f(x+1)=\frac12(x+1)=\frac12x+\frac12\qquad\text{shift up }\frac12
\]

None of these could possibly look exponential - they are all linear, and can be seen as shifts up and down (or left and right).

Is the function \(f(x)\) different?