Question Type 5: Drawing the effect of multiple transformations on a graph Exercises

Let $f(x)=x^2$. Sketch the graph of $g(x)=-2\,f\left(\frac{x}{3}-1\right)+5$, 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 $y = \tfrac12(x + 3)^2 - 2$.

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.