Graph transformations, gradients of curves and areas under graphs

By the end you’ll be able to

• Identify and sketch the translations $y = f(x) + a$ and $y = f(x + a)$ and the reflections $y = -f(x)$ and $y = f(-x)$, and state the effect on key points (Higher)
• Estimate the gradient of a curve at a point by drawing a tangent, and interpret it as an instantaneous rate of change (Higher)
• Estimate the area under a curve using trapezia or strips, interpret it (e.g. distance travelled), and say whether it is an over- or underestimate (Higher)