Pre-Calc Unit 2

19 flashcards · Mathematics · by Logan Pollack

1. Vertex Form of Quadratic Function

   f(x)=a(x−h)2+kf(x) = a(x-h)^2 + kf(x)=a(x−h)2+k

2. Vertex Form of Absolute Value Function

   f(x)=a∣x−h∣+kf(x) = a|x-h| + kf(x)=a∣x−h∣+k

3. Vertex Form of Square Root Function

   f(x)=ax−h+kf(x) = a \sqrt{x-h} + kf(x)=ax−h ​+k

4. The Parent Graph of a function refers to the functions above (Square Root, Absolute Value, Quadratic) in which a = 1, h = 0, and k = 0

5. Parent Graph of a Quadratic Function

   y=x2y=x^2y=x2

6. Parent Graph of an Absolute Value Function

   y=∣x∣y = |x|y=∣x∣

7. Parent Graph of a Square Root Function

   y=xy = \sqrt{x}y=x ​

8. All horizontal and vertical translations along with reflections are known as Rigid Transformations because the size and shape of the graph remain unchanged.

9. Stretches and shrinks are known as Nonrigid Transformations because the size and shape of the graph have been changed

10. Given a function, f(x)f(x)f(x) , the graph of h(x)=f(x)+ch(x) = f(x) + ch(x)=f(x)+c will be

    shifted up c units

11. Given a function, f(x)f(x)f(x) , the graph of h(x)=f(x)−ch(x) = f(x) - ch(x)=f(x)−c will be

    shifted down c units

12. Given a function, f(x)f(x)f(x) , the graph of h(x)=f(x+c)h(x) = f(x + c)h(x)=f(x+c) will be

    shifted to the left c units

13. Given a function, f(x)f(x)f(x) , the graph of h(x)=f(x−c)h(x) = f(x-c)h(x)=f(x−c) will be

    shifted to the right c units

14. Given a function, f(x)f(x)f(x) , the graph of h(x)=−f(x)h(x) = -f(x)h(x)=−f(x) will be

    reflected over the x-axis

15. Given a function, f(x)f(x)f(x) , the graph of h(x)=f(−x)h(x) = f(-x)h(x)=f(−x) will be

    reflected over the y axis

16. Given a function, f(x)f(x)f(x) , the graph of 1"> h(x)=cf(x),c>1h(x) = cf(x), c>1h(x)=cf(x),c>1 , will

    vertically stretch

17. Given a function, f(x)f(x)f(x) , the graph of h(x)=cf(x),0<c<1h(x) = cf(x), 0<c<1h(x)=cf(x),0<c<1 , will

    vertically shrink

18. Given a function, f(x)f(x)f(x) , the graph of 1"> h(x)=f(cx),c>1h(x) = f(cx), c>1h(x)=f(cx),c>1 , will

    horizontally shrink

19. Given a function, f(x)f(x)f(x) , the graph of h(x)=f(cx),0<c<1h(x) = f(cx), 0<c<1h(x)=f(cx),0<c<1 , will

    horizontally stretch