Pre-Calc Unit 1

19 flashcards · Mathematics · by Logan Pollack

1. A function is increasing when...

   it is going up

2. a function is decreasing when...

   it is going down

3. a function is constant when...

   it is horizontal

4. The slope of a non-vertical line passing through two points, (x1,y1)(x_1,y_1)(x1​,y1​) and (x2,y2)(x_2, y_2)(x2​,y2​) is given by

   y2−y1x2−x1=m\frac{y_2-y_1}{x_2-x_1} = mx2​−x1​y2​−y1​​=m

5. slope-intercept form

   y=mx+by=mx+by=mx+b

6. point-slope form

   y−y1=m(x−x1)y-y_1 = m(x-x_1)y−y1​=m(x−x1​)

7. horizontal line equation

   y=ky=ky=k

8. vertical line equation

   x=hx=hx=h (not a function)

9. Parallel Lines Slope

   Slopes of parallel lines are the same

10. Perpendicular Lines Slope

    Slopes are opposite reciprocals

11. The equation of a circle with a center (h,k) and radius r is

    (x−h)2+(y−k)2=r2(x-h)^2 + (y-k)^2 = r^2(x−h)2+(y−k)2=r2

12. Any point that lies on the graph of a function is called a solution point since its coordinates will be a solution of the equation of the function

13. x-intercepts

    the points where a graph crosses the x-axis. Substitute 0 for y, solve for x. X-intercepts are written as an ordered pair

14. y-intercepts

    The point where a graph crosses the y-axis. Substitute 0 for x, solve for y. Y-intercepts are written as an ordered pair. If there are multiple y-intercepts the graph is not a function

15. Algebraic Tests for Symmetry x-axis if replacing:

    y with -y yields an equivalent equation when solved for y

16. Algebraic Tests for Symmetry y-axis if replacing:

    x with -x yields an equivalent equation when solved for y

17. Algebraic Tests for Symmetry y=xy=xy=x if replacing:

    x with y and y with x yields and equivalent equation

18. Algebraic Tests for Symmetry Origin if replacing

    x with -x and y with -y yields an equivalent equation when solved for y

19. Symmetry

    The most common type of symmetry in graphs are line symmetry, and it may be with respect to the x or y axes, or the line y=xy=xy=x . Another common type of symmetry is point symmetry with respect to the origin When you fold the Cartesian plane with respect to a line (such as the x-axis), a graph contains line symmetry (with respect to that line) if the two portions of the graph coincide.