Use and interpret function notation · lesson

Evaluating f(x)

💡 f(3) means replace every x in the rule with 3, then compute.

f(x) is read "f of x". It does not mean f times x. It names the output of rule f for input x.

To find f(−1), put −1 in for every x. Use parentheses around negatives so the signs stay right.

Remember the order of operations: exponents before multiplying.

🧠 Let's work it out

f(x) = 2x² − x + 3. Find f(−1).

What do you think comes next?

💡 In a real-world function, the input and output have units, so read what each one means before you compute.

Formulas often use letters that hint at their meaning: c(n) for the cost of n items, h(t) for height at time t.

If you're given the input, evaluate. If you're given the output, set the rule equal to it and solve for the input.

🧠 Let's work it out

c(n) = 8n + 20 is the cost in dollars of n shirts. Find c(4).

What do you think comes next?

💡 Evaluate each function on its own first, then add, subtract, or feed one output into the next function.

f(3) + g(3) means find each output, then add them.

f(f(1)) means work from the inside out. Find f(1), then put that answer back into f.

f(a + 2) means put the whole expression a + 2 in for x.

🧠 Let's work it out

f(x) = x + 4. Find f(f(1)).

What do you think comes next?

💡 If you know f(x)'s value, set the rule equal to that value and solve for x.

"g(a) = 23" means the output is 23. Set the rule equal to 23 and solve.

"f(x) = x" means the output equals the input. Set the rule equal to x and solve.

🧠 Let's work it out

g(x) = 4x + 3 and g(a) = 23. Find a.

What do you think comes next?