AS Pure Chapter 4: Graphs and Transformations

13 flashcards · Mathematics · by TheoTyson

1. What is the form of a cubic function?

   ax3+bx2+cx+dax^3 + bx^2 + cx + dax3+bx2+cx+d where a,b,ca, b, ca,b,c and ddd are real numbers and a≠0a \neq 0a=0

2. What is the form of a quartic function?

   ax4+bx3+cx2+dx+eax^4 + bx^3 + cx^2 + dx + eax4+bx3+cx2+dx+e where a,b,c,da, b, c, da,b,c,d and eee are real numbers and a≠0a \neq 0a=0

3. What are the asymptotes of reciprocal graphs?

   x=0x=0x=0 and y=0y=0y=0 .

4. What is the graph of y=kxy=\frac{k}{x}y=xk​ with 0"> k>0k > 0k>0 ?

5. What is the graph of y=kxy = \frac{k}{x}y=xk​ with k<0k < 0k<0 ?

6. What is the graph of y=kx2y = \frac{k}{x^2}y=x2k​ with 0"> k>0k>0k>0 ?

7. What is the graph of y=kx2y = \frac{k}{x^2}y=x2k​ with k<0k < 0k<0 ?

8. What is the transformation described by y=f(x)+ay = \text{f}(x) + ay=f(x)+a ?

   Move the graph of y=f(x)y = \text{f}(x)y=f(x) up or down by aaa units.

9. What is the transformation described by y=f(x+a)y = \text{f}(x+a)y=f(x+a) ?

   Move the graph of y=f(x)y = \text{f}(x)y=f(x) left or right by −a-a−a units.

10. What is the transformation described by y=af(x)y = a \text{f}(x)y=af(x) ?

    A stretch of the graph y=f(x)y = \text{f}(x)y=f(x) by a scale factor aaa in the vertical direction.

11. What is the transformation described by y=f(ax)y = \text{f}(ax)y=f(ax) ?

    A stretch of the graph y=f(x)y = \text{f}(x)y=f(x) by a scale factor 1a\frac{1}{a}a1​ in the horizontal direction.

12. What is the transformation described by y=−f(x)y = -\text{f}(x)y=−f(x)

    A reflection of the graph y=f(x)y = \text{f}(x)y=f(x) in the xxx -axis.

13. What is the transformation described by y=f(−x)y = \text{f}(-x)y=f(−x)

    A reflection of the graph y=f(x)y = \text{f}(x)y=f(x) in the yyy -axis.