Question Type 1: Drawing the effect of single transformations on a graph Exercises

Sketch the graph of $g(x)=2|x|$ by applying a vertical stretch of factor 2 to $f(x)=|x|$. Label the vertex and two other points.

Given $f(x)=x^2+2$, draw the graph of the function after reflecting $f$ in the x-axis. Label key points.

Given $f(x)=x^2+1$, sketch the graph of the function obtained by applying a vertical stretch of factor 3 to $f$. Label the new vertex and two other points.

For $f(x)=x^2-3$, sketch the graph of the function after a vertical stretch by factor 5. Label the vertex and two more points.

Sketch the graph of the function obtained by a horizontal compression of factor 3 of $f(x)=x^2$. Label the vertex and two other symmetric points.

Sketch the graph of $g(x)=4\bigl(x^2-2\bigr)$. Clearly label the vertex and two additional points on each side of the axis of symmetry.

Let $f(x)=x^2-4$. Draw the graph of the function obtained by a horizontal stretch of factor 2 applied to $f$. Label the vertex and two other points.

For $f(x)=x^2$, determine whether a horizontal stretch by factor $\frac12$ and a vertical stretch by factor 4 produce the same transformed graph. Justify your answer.

Determine whether applying a horizontal stretch of factor $\tfrac14$ to $f(x)=x^2$ yields the same graph as a vertical stretch by factor 16. Provide a short proof.

Determine whether the following two transformations of $f(x)=x^2$ produce the same graph:

(1) a horizontal stretch by factor 4;
(2) a vertical stretch by factor 16.
Explain your reasoning.

For $f(x)=x^2-1$, decide if a horizontal stretch by factor 5 on the graph of $f$ is equivalent to a vertical stretch by factor 25. Show all steps.

Check if a horizontal compression by factor 3 of $f(x)=x^2$ is equivalent to a vertical stretch by factor 9. Justify.

Is a horizontal compression by factor 2 of $f(x)=x^2$ the same transformation as a vertical stretch by factor 4? Justify your answer.