Question

HELP!!! SEE ATTACHED

Answer 1

Answer should be

The slope of the tangent line to the function at x = a is 2.
slope of line through points [x, f(x)] and [ a, f(a)]

Answer 2

Step-by-step explanation:

The given expression is

$\frac{f(b)-f(a)}{b-a}=2$

Notice that $a$ and $b$ are elements of the domain and $f(a)$ and $f(b)$ are elements of the range.

Observe the notation used,  an element of the range is always written like $f(x)$ where $x$ is an element of the domain.

Also, notice that this expression is using two pair of coordinates, which are $(a, f(a))$ and $(b,f(b))$.

On the other hand, the definition of average rate of change is

$r=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }$

Where $(x_{1} ,y_{1} )=(a ,f(a))$ and $(x_{2} ,y_{2} )=(b ,f(b))$.

Having said that, the given expression represents an average rate of change in the interval, where the rate is 2. The right answer is the third option.