Question

How do you graph `y=sectheta+2`?

Answer 1

See below.

Explanation:

1. Graph the function first as if it were a cosine function. This is because secant is the inverse of cosine.
2. Begin with the reference y= d+a cos (bx-c).
3. The absolute value of a is your amplitude (in this case, it's an understood 1). This is one-half the distance between the highest and lowest points of the graph.
4. If graphing in degrees, your period is 360/b, or in this case 360. (If in radians, use 2`pi`, which is equivalent to 360 degrees).
5. The horizontal translation, or phase shift, is equal to -c/b. In this case, it's 0 because there is no c or b. There is no horizontal translation.
6. The vertical translation is equal to d, or in this case, +2.
7. Graph it like a COSINE function.
8. Make a t-table with your points.
9. Your first point is equal to your horizontal translation, or in this case 0.
10. Your end point is equal to your horizontal translation plus your period, or in this case, 360 (or 2`pi` if graphing in radians).
11. Your increments are gained by dividing your period by 4. (in this case, 90).
12. Your points on the x side of your t-table will be 0, 90, 180, 270, and 360 in this case. That is one full cycle of the function.
13. Use a calculator to get your y points, being careful with parentheses. If you can't use a calculator, do translations on the parent function. y=cos(x)
14. Graph the COSINE function, but don't connect the dots.
15. Every HIGH point on the graph will be a parabola opening UP.
16. Every LOW point on the graph will be a parabola opening DOWN.
17. Every MIDDLE point is an asymptote . Draw a vertical dashed line here.
18. You've now graphed a secant graph with a vertical translation of +2!