Secant Graphs: Period, Asymptotes, Shifts & Range Quiz

Reviewed by Editorial Team
The ProProfs editorial team is comprised of experienced subject matter experts. They've collectively created over 10,000 quizzes and lessons, serving over 100 million users. Our team includes in-house content moderators and subject matter experts, as well as a global network of rigorously trained contributors. All adhere to our comprehensive editorial guidelines, ensuring the delivery of high-quality content.
Learn about Our Editorial Process
| By Thames
T
Thames
Community Contributor
Quizzes Created: 7116 | Total Attempts: 9,522,086
| Questions: 20 | Updated: Oct 31, 2025
Please wait...
Question 1 / 20
0 %
0/100
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)
We’ll put your name on your report, certificate, and leaderboard.
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
View My Results
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?
Alert!

Back to Top Back to top
Advertisement