The image you've uploaded discusses the evaluation of functions, specifically showing how to substitute a value for $x$ in a function.

Concept Notes:

• Evaluating a function involves replacing the variable in the function with a specific value and computing the result.
• For example, the given function is $f(x) = 2x + 1$. If you need to evaluate it at $x = 3$, you substitute 3 into the function: $f(3) = 2(3) + 1 = 6 + 1 = 7$

Example:

• Function: $f(x) = 2x + 1$
• Evaluate for $x = 3$:

Solution steps:

1. $f(3) = 2(3) + 1$
2. $f(3) = 6 + 1$
3. $f(3) = 7$

Exercises:

The two given exercises are:

1. Evaluate $f(x) = 2x$ at $x = 3$
2. Evaluate $f(x) = 2x - 7$ at $x = 4$

Would you like to solve these exercises with detailed steps?

Here are 5 related questions to expand your understanding:

1. What happens to the function's output if we increase the value of $x$ in $f(x) = 2x + 1$?
2. How would you evaluate the function $f(x) = 3x^2 + 4x - 5$ at $x = 2$?
3. What is the meaning of the domain of a function when evaluating it?
4. How would the function change if you replaced $2x$ with $x^2$ in $f(x) = 2x + 1$?
5. Can a function be evaluated for a non-numerical input? If so, what type of function would allow that?

Tip: Always substitute values carefully and simplify the expression step by step to avoid mistakes.