Given the function $$ f(x)=4 x-4 $$, evaluate and simplify the expressions below. See special instructions on how to enter your answers. $$ f(a)= $$ $$ f(a+h)= $$ $$ \frac{f(a+h)-f(a)}{h}=\square $$ lnstructions: Simplify answers as much as possible. Expressions such as $$ 4(x+2) $$ and $$ (x+5)^{2} $$ should be expanded. Also collect like terms, so $$ 3 x+x $$ should be written as $$ 4 x $$.

Question

UpStudy AI · Accepted Answer

Let's evaluate and simplify each expression step by step for the function $$ f(x) = 4x - 4 $$.

1. **Evaluate $$ f(a) $$:**
   $$
   f(a) = 4a - 4
   $$
   This is already simplified.

2. **Evaluate $$ f(a+h) $$:**
   $$
   f(a+h) = 4(a + h) - 4
   $$
   Expand the expression:
   $$
   f(a+h) = 4a + 4h - 4
   $$
   This is the simplified form.

3. **Evaluate $$ \frac{f(a+h) - f(a)}{h} $$:**
   $$
   \frac{f(a+h) - f(a)}{h} = \frac{(4a + 4h - 4) - (4a - 4)}{h}
   $$
   Simplify the numerator:
   $$
   \frac{4a + 4h - 4 - 4a + 4}{h} = \frac{4h}{h}
   $$
   Cancel the $$ h $$ terms:
   $$
   \frac{4h}{h} = 4
   $$

**Final Answers:**
$$
f(a) = 4a - 4
$$
$$
f(a+h) = 4a + 4h - 4
$$
$$
\frac{f(a+h) - f(a)}{h} = 4
$$
$$ f(a) = 4a - 4 $$ $$ f(a+h) = 4a + 4h - 4 $$ $$ \frac{f(a+h) - f(a)}{h} = 4 $$

Real Tutor Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Algebra Questions