Secant Graphs: Period, Asymptotes, Shifts & Range Quiz

  • 11th Grade
Reviewed by Cierra Henderson
Cierra Henderson, MBA |
K-12 Expert
Review Board Member
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
 , MBA
By Thames
T
Thames
Community Contributor
Quizzes Created: 8156 | Total Attempts: 9,588,805
| Questions: 20 | Updated: Jan 22, 2026
Please wait...
Question 1 / 21
🏆 Rank #-- ▾
Score 0/100

1) What is the relationship between the secant function and the cosine function?

Explanation

Secant is defined as the reciprocal of cosine.

So, sec(x) = 1/cos(x).

Submit
Please wait...
About This Quiz
Secant Graphs: Period, Asymptotes, Shifts & Range Quiz - Quiz

See how secant rides on cosine! You’ll use the reciprocal relationship to place vertical asymptotes where cosine is zero, find the U-shaped branches, and read the period, shifts, and reflections from the equation. By the end, you’ll graph secant confidently—fast.

2)

What first name or nickname would you like us to use?

You may optionally provide this to label your report, leaderboard, or certificate.

2) What is the period of y = sec(x)?

Explanation

Step 1: Secant shares cosine’s period.

Step 2: Period of cosine is 2π.

So, the period is 2π.

Submit

3) At which values of x does y = sec(x) have vertical asymptotes?

Explanation

Step 1: sec(x)=1/cos(x) is undefined when cos(x)=0.

Step 2: cos(x)=0 at x=π/2 + nπ.

Submit

4) What is the range of y = sec(x)?

Explanation

Given: sec(x) = 1/cos(x).

Step 1: cos(x) takes values between −1 and 1.

Step 2: The reciprocal is ≤ −1 or ≥ 1.

So, the final answer is (−∞, −1] ∪ [1, ∞).

Submit

5) What is the period of y = sec(2x)?

Explanation

Given: y = sec(bx).

Step 1: The period = 2π/|b|.

Step 2: Here, b = 2 ⇒ Period = π.

So, the final answer is π.

Submit

6) The graph of y = sec(x) is undefined where:

Explanation

Given: sec(x) = 1/cos(x).

Step 1: Undefined when denominator = 0.

So, the final answer is cos(x) = 0.

Submit

7) Which transformation produces y = −2 sec(x − π/3) + 1 from y = sec(x)?

Explanation

Step 1: “−” ⇒ reflect over x-axis.

Step 2: “2” ⇒ vertical stretch by 2.

Step 3: “x − π/3” ⇒ shift right π/3.

Step 4: “+1” ⇒ shift up 1.

So, the final answer is reflect x-axis, stretch 2, right π/3, up 1.

Submit

8) What is the phase shift of y = sec(x + π/4)?

Explanation

Given: x + π/4.

Step 1: A plus inside moves the graph left.

So, the final answer is left π/4.

Submit

9) The vertical asymptotes of y = sec(3x) occur at:

Explanation

Step 1: cos(3x) = 0 ⇒ 3x = π/2 + nπ.

Step 2: Divide by 3 ⇒ x = π/6 + nπ/3.

So, the final answer is x = π/6 + nπ/3.

Submit

10) The graph of y = a sec(bx) has period 2π/|b|. If its period is 4π, what is b?

Explanation

Step 1: 2π/|b| = 4π.

Step 2: |b| = ½.

So, the final answer is b = ½.

Submit

11) Which statement about y = sec(x) is true?

Explanation

Test parity → sec(−x) = 1/cos(−x) = 1/cos x = sec x.

So, the final answer is even.

Submit

12) For y = sec(x), which intervals contain U-shaped branches opening upward?

Explanation

sec(x) = 1/cos(x) > 0 when cos(x) > 0.

So, the final answer is on intervals where cos(x) > 0.

Submit

13) Consider y = 3 sec(x) − 2. What is its range?

Explanation

Step 1: Base sec range is ≤ −1 or ≥ 1.

Step 2: ×3 ⇒ ≤ −3 or ≥ 3.

Step 3: −2 shift ⇒ ≤ −5 or ≥ 1.

So, the final answer is (−∞, −5] ∪ [1, ∞).

Submit

14) The reciprocal identity that helps plot secant given cosine is:

Explanation

Multiply sec x = 1/cos x by cos x.

So, the final answer is sec(x) cos(x) = 1.

Submit

15) Which function has the same vertical asymptotes as y = sec(x)?

Explanation

Step 1: tan(x) = sin(x)/cos(x).

Step 2: Undefined when cos x = 0, same as sec.

So, the final answer is y = tan(x).

Submit

16) If y = sec(x) is reflected across the y-axis, the resulting graph is:

Explanation

Step 1: Replace x by −x for y-axis reflection.

Step 2: sec(−x) = sec(x) since it’s even.

So, the final answer is y = sec(−x).

Submit

17) The reciprocal of y = 2 cos(x) is:

Explanation

1/(2 cos x) = (1/2)·(1/cos x) = (1/2) sec x.

Submit

18) The vertical asymptotes of y = sec(x − π/4) are at:

Explanation

Step 1: cos(x − π/4) = 0 ⇒ x − π/4 = π/2 + nπ.

Step 2: x = 3π/4 + nπ.

So, the final answer is x = 3π/4 + nπ.

Submit

19) Which best describes the graph of y = −sec(x)?

Explanation

Negative sign reflects across x-axis.

So, the final answer is reflection across x-axis.

Submit

20) Which statement about y = sec(x) and y = cos(x) is correct?

Explanation

Step 1: Both have period 2π.

Step 2: Sec undefined when cos = 0.

So, the final answer is same periods; sec undefined where cos = 0.

Submit
×
Saved
Thank you for your feedback!
View My Results
Cierra Henderson |MBA |
K-12 Expert
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
Cancel
  • All
    All (20)
  • Unanswered
    Unanswered ()
  • Answered
    Answered ()
What is the relationship between the secant function and the cosine...
What is the period of y = sec(x)?
At which values of x does y = sec(x) have vertical asymptotes?
What is the range of y = sec(x)?
What is the period of y = sec(2x)?
The graph of y = sec(x) is undefined where:
Which transformation produces y = −2 sec(x − π/3) + 1...
What is the phase shift of y = sec(x + π/4)?
The vertical asymptotes of y = sec(3x) occur at:
The graph of y = a sec(bx) has period 2π/|b|. If its period is...
Which statement about y = sec(x) is true?
For y = sec(x), which intervals contain U-shaped branches opening...
Consider y = 3 sec(x) − 2. What is its range?
The reciprocal identity that helps plot secant given cosine is:
Which function has the same vertical asymptotes as y = sec(x)?
If y = sec(x) is reflected across the y-axis, the resulting graph is:
The reciprocal of y = 2 cos(x) is:
The vertical asymptotes of y = sec(x − π/4) are at:
Which best describes the graph of y = −sec(x)?
Which statement about y = sec(x) and y = cos(x) is correct?
play-Mute sad happy unanswered_answer up-hover down-hover success oval cancel Check box square blue
Alert!