Question
Sketch the graph of each function by transforming the graph of an appropriate function of the form $y=x^{n}$ from Figure $1 .$ Indicate all $x$ - and $y$ -intercepts on each graph.a. $P(x)=x^{2}-4$b. $Q(x)=(x-4)^{2}$c. $P(x)=2 x^{2}+3$d. $P(x)=-(x+2)^{2}$
Step 1
The function $P(x)=x^{2}-4$ is a transformation of the function $y=x^{2}$, where the graph is shifted down by 4 units. Show more…
Show all steps
Your feedback will help us improve your experience
Ankit Gupta and 55 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Sketch the graph of each function by transforming the graph of an appropriate function of the form $y=x^{n}$ from Figure $2 .$ Indicate all $x-$ and $y$ -intercepts on each graph. $$\begin{array}{ll}{\text { (a) } P(x)=x^{2}-4} & {\text { (b) } Q(x)=(x-4)^{2}} \\ {\text { (c) } R(x)=2 x^{2}-2} & {\text { (d) } S(x)=2(x-2)^{2}}\end{array}$$
Polynomial and Rational Functions
Polynomial Functions and Their Graphs
Sketch the graph of each function by transforming the graph of an appropriate function of the form $y=x^{n}$ from Figure $2 .$ Indicate all $x-$ and $y$ -intercepts on each graph. $$ \begin{array}{l}{\text { (a) } P(x)=x^{4}-16 \quad \text { (b) } Q(x)=(x+2)^{4}} \\ {\text { (c) } R(x)=(x+2)^{4}-16 \text { (d) } S(x)=-2(x+2)^{4}}\end{array} $$
Sketch the graph of each function by transforming the graph of an appropriate function of the form $y=x^{n}$ from Figure $2 .$ Indicate all $x-$ and $y$ -intercepts on each graph. $$ \begin{array}{ll}{\text { (a) } P(x)=x^{3}-8} & {\text { (b) } Q(x)=-x^{3}+27} \\ {\text { (c) } R(x)=-(x+2)^{3}} & {\text { (d) } S(x)=\frac{1}{2}(x-1)^{3}+4}\end{array} $$
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD