IB Mathematics Applications & Interpretation Question Type 5: Drawing the Effect of Multiple Transformations on a Graph Exercises

Let $f(x)=x^2$. Sketch the graph of $g(x)=-2f\left(\frac{x}{3}-1\right)+5$, which can be written as $g(x)=-2{\left(\frac{x}{3}-1\right)}^2+5$.

Sketch the graph of $y=-x^2$.

Sketch the graph of $y=(x-3{)}^2$.

Sketch the graph of $y=-2(x+2{)}^2+3$.

Sketch the graph of $y=(x+2{)}^2+1$.

Sketch the graph of $y=x^2+4$.

Sketch the graph of $y=\frac{1}{2}(x+3{)}^2-2$.

Sketch the graph of $y=-3(x-1{)}^2$.

Draw and label the graph of $y=4(x-1{)}^2-6$ using $y=x^2$ as the base curve.

Sketch the graph of $y=2x^2-5$.

Given the curve $y=x^2-2$, sketch and label the graph of $y=-\frac{1}{2}(x+1{)}^2+4$ relative to it.

Sketch the graph of $y=f(x)$, clearly showing the vertex and at least one other point.