Find and simplify each of the following for $f(x)=2 x-5$
(A) $f(x+h)$
(B) $f(x+h)-f(x)$
(C) $\frac{f(x+h)-f(x)}{h}$

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Steps

Step 1 ：Substitute $x+h$ into the function $f(x) = 2x - 5$ to get $f(x+h) = 2(x+h) - 5 = 2h + 2x - 5$

Step 2 ：Find the difference between $f(x+h)$ and $f(x)$ to get $f(x+h) - f(x) = (2h + 2x - 5) - (2x - 5) = 2h$

Step 3 ：Divide the difference found in the previous step by $h$ to get $\frac{f(x+h) - f(x)}{h} = \frac{2h}{h} = 2$

Step 4 ：$\boxed{\text{Final Answer:}}$

Step 5 ：(A) $\boxed{f(x+h) = 2h + 2x - 5}$

Step 6 ：(B) $\boxed{f(x+h) - f(x) = 2h}$

Step 7 ：(C) $\boxed{\frac{f(x+h) - f(x)}{h} = 2}$