Conclude by giving your students these challenges:

- Marbles and Bags by NRICH
- Starfish Spotting by NRICH
- A Biggy by NRICH
- Alphabet Soup by NRICH
- Iterated Function Domain
- A Cross-Section Area

Conclude by giving your students these challenges:

- Marbles and Bags by NRICH
- Starfish Spotting by NRICH
- A Biggy by NRICH
- Alphabet Soup by NRICH
- Iterated Function Domain
- A Cross-Section Area

Let \(f(x) = 7x\) and \(h \ne 0\). Simplify:
$$\dfrac{f(x + h) - f(x)}{h}$$

\(7\)

Let \(f(x) = 5x + 4\) and \(h \ne 0\). Simplify:
$$\dfrac{f(x + h) - f(x)}{h}$$

\(5\)

Let \(f(x) = x^2\) and \(h \ne 0\). Simplify:
$$\dfrac{f(x + h) - f(x)}{h}$$

\(2x + h\)

Let \(f(x) = \sqrt{x}\) and \(h \ne 0\). Simplify:
$$\dfrac{f(x + h) - f(x)}{h}$$

\(\dfrac{1}{\sqrt{x + h} + \sqrt{x}}\)

Let \(f(x) = \dfrac{1}{x}\) and \(h \ne 0\). Simplify:
$$\dfrac{f(x + h) - f(x)}{h}$$

\(\dfrac{-1}{x(x + h)}\)

Let \(f(x) = 3x^2 + 4x - 5\) and \(h \ne 0\). Simplify:
$$\dfrac{f(x + h) - f(x)}{h}$$

\(6x + 3h + 4}\)

Let \(f(x) = 4x^2 - 2x\) and \(h \ne 0\). Simplify:
$$\dfrac{f(x + h) - f(x)}{h}$$

\(4h + 8x - 2\)

Let \(f(x) = 3x^2 + 2x\) and \(h \ne 0\). Simplify:
$$\dfrac{f(x + h) - f(x)}{h}$$

\(3h + 6x + 2\)

Let \(f(x) = x^3\) and \(h \ne 0\). Simplify:
$$\dfrac{f(x + h) - f(x)}{h}$$

\(3x^2 + 3xh + h^2\)

Let \(f(x) = x^2 - x + 1\) and \(h \ne 0\). Simplify:
$$\dfrac{f(2 + h) - f(2)}{h}$$

\(h + 3\)