Unlock hundreds more features
Save your Quiz to the Dashboard
View and Export Results
Use AI to Create Quizzes and Analyse Results

OR
Sign inSign in with Facebook
Sign inSign in with Google
Quizzes > High School Quizzes > Mathematics

Practice Quiz: Piecewise Function Word Problems

Sharpen skills with engaging exam practice tests

Difficulty: Moderate
Grade: Grade 10
Study OutcomesCheat Sheet
Colorful paper art promoting Piecewise Function Frenzy, a trivia quiz for high school algebra students.

For the piecewise function f(x) = { 2x + 1 if x < 3, x² if x ≥ 3 }, what is f(4)?
16
2
9
7
Since 4 is greater than or equal to 3, the rule f(x) = x² applies. Substituting 4 into that expression gives 4², which equals 16.
For the piecewise function g(x) = { x - 5 if x ≤ 2, 3x + 1 if x > 2 }, what is g(2)?
-3
5
7
3
At x = 2 the condition x ≤ 2 holds, so we use the first piece: g(2) = 2 - 5 = -3. Thus, the correct answer is -3.
Consider the function h(x) = { 4 if x < 0, x² if x ≥ 0 }. What is h(-2)?
-2
4
2
0
Since -2 is less than 0, the function returns the constant value 4 regardless of x. Therefore, h(-2) is 4.
Let f(x) = { 3x + 2 for x < 1, 2x - 1 for x ≥ 1 }. What is f(1)?
3
2
1
0
Because x = 1 satisfies the condition x ≥ 1, we apply the rule f(x) = 2x - 1. Substituting 1 gives 2(1) - 1 = 1.
Evaluate the function p(x) = { x² if x < 0, 0 if x = 0, x if x > 0 }. What is p(0)?
1
p(0) is undefined
0
-1
The function explicitly defines p(0) as 0 when x equals 0. There is no calculation needed with the other pieces because the condition is directly provided.
Determine if the piecewise function f(x) = { x + 4 if x < 2, 3x - 2 if x ≥ 2 } is continuous at x = 2.
Continuous at x = 2
Continuous only for x < 2
Continuous only for x > 2
Discontinuous at x = 2
At x = 2, the left-hand limit (2 + 4) and the right-hand limit (3Ã - 2 - 2) both equal 6, confirming that the function is continuous at that point.
Given f(x) = { 2x - 3 for x < 0, x² for x ≥ 0 }, what is the value of f(0)?
2
Undefined
0
-3
Since 0 satisfies the condition x ≥ 0, we use the rule f(x) = x². Thus, f(0) = 0² = 0.
For the function f(x) = { x² if x < 5, 2x + 1 if x ≥ 5 }, what is f(5)?
11
10
5
25
At x = 5 the condition x ≥ 5 applies, which means we calculate f(5) using 2x + 1. Substituting 5 gives 2(5) + 1 = 11.
Determine the domain of the function f(x) = { 1/(x - 3) if x < 3, x + 2 if x ≥ 3 }.
x < 3
x ≠3
x > 3
All real numbers
For x < 3, the term 1/(x - 3) is defined because x never equals 3; for x ≥ 3, x + 2 is defined for all x. Thus, every real number is included in the domain.
For the piecewise function f(x) = { 3x + 2 for x ≤ 1, 2x - 1 for x > 1 }, find all values of x such that f(x) equals 5.
x = 1 and x = 3
x = 1
x = 3
x = 3 only
Solving 3x + 2 = 5 for x ≤ 1 gives x = 1, and solving 2x - 1 = 5 for x > 1 gives x = 3. Both solutions satisfy their respective conditions.
For the function f(x) = { |x| if x < 0, 2x - 1 if x ≥ 0 }, what is f(-3)?
6
0
-3
3
Since -3 is less than 0, we apply the absolute value function. The absolute value of -3 is 3, making 3 the correct result.
Determine f(2) for the function f(x) = { x - 1 if x < 2, 3 if x = 2, 2x + 1 if x > 2 }.
3
5
1
4
The function directly specifies that when x = 2, f(x) is equal to 3. Thus, regardless of the other expressions, f(2) is 3.
For the function f(x) = { 5 if x < 0, x² if 0 ≤ x < 4, 2x - 3 if x ≥ 4 }, what is f(3)?
3
5
9
1
Since 3 falls in the interval 0 ≤ x < 4, we use the second piece to evaluate f(3) as 3², which equals 9.
Given the piecewise function f(t) = { t + 2 if t < 5, 3t - 7 if t ≥ 5 }, what is f(5)?
10
7
8
5
At t = 5 the condition t ≥ 5 applies, so f(5) is calculated as 3(5) - 7, which simplifies to 8.
For the function f(x) = { 2x + 10 if x ≤ 0, 3x² if x > 0 }, what is f(-2)?
10
6
2
-6
Since -2 falls under the condition x ≤ 0, the correct piece is f(x) = 2x + 10. Plugging in -2 results in 2(-2) + 10, which equals 6.
Determine the points of discontinuity for the function f(x) = { 1/(x - 2) if x < 2, (x² - 4)/(x - 2) if x ≥ 2 }.
x = -2
x = 2
x = 2 and x = -2
None
For x ≥ 2, the expression (x² - 4)/(x - 2) becomes indeterminate at x = 2, and x = 2 also marks the boundary of the pieces. Therefore, the function is discontinuous at x = 2.
A shipping company charges based on weight according to C(w) = { 10 if w ≤ 2, 10 + 2(w - 2) for 2 < w ≤ 5, 16 + 3(w - 5) for w > 5 }. What is the shipping cost for a 4 kg package?
14
18
16
10
A 4 kg package fits in the range 2 < w ≤ 5. The cost is calculated as 10 + 2(4 - 2) = 10 + 4, which totals 14.
The function f(x) = { x + 5 if x < k, 3x - 1 if x ≥ k } is continuous. What is the value of k?
5
4
3
2
For continuity at x = k, the two expressions must meet, so set k + 5 = 3k - 1. Solving this yields k = 3.
Consider the function f(x) = { 2x² - 3 if x < 1, ax + b if x ≥ 1 } which is continuous and satisfies f(1) = -1. What is the value of a + b?
-1
0
2
1
Continuity at x = 1 requires that the left-hand limit, 2(1)² - 3 = -1, matches the value from the second piece, which is a + b. Therefore, a + b must be -1.
A taxi service uses the fare function F(d) = { 3 + 2d if d ≤ 5, 3 + 10 + 1.5(d - 5) if d > 5 } where d is the distance in kilometers. What is the fare for a 7 km ride?
13
16
18
14
Since 7 km exceeds 5 km, the second formula applies. Calculating gives 3 + 10 + 1.5(7 - 5) = 13 + 3 = 16.
0
{"name":"For the piecewise function f(x) = { 2x + 1 if x < 3, x² if x ≥ 3 }, what is f(4)?", "url":"https://www.quiz-maker.com/QPREVIEW","txt":"For the piecewise function f(x) = { 2x + 1 if x < 3, x² if x ≥ 3 }, what is f(4)?, For the piecewise function g(x) = { x - 5 if x ≤ 2, 3x + 1 if x > 2 }, what is g(2)?, Consider the function h(x) = { 4 if x < 0, x² if x ≥ 0 }. What is h(-2)?","img":"https://www.quiz-maker.com/3012/images/ogquiz.png"}

Study Outcomes

  1. Analyze and interpret the components of piecewise functions.
  2. Apply appropriate methods to solve piecewise function word problems.
  3. Evaluate the behavior of piecewise functions across different intervals.
  4. Construct piecewise functions based on given problem conditions.
  5. Demonstrate proficiency in transitioning between different function expressions.

Piecewise Function Word Problems Cheat Sheet

  1. Grasp the piecewise concept - Think of a piecewise function as a cool multi-part playlist where each "track" (sub-function) plays only on its own interval, modeling different behaviors at different spots. This lets you tailor functions to real-life changes, like speed limits switching on different road segments. Piecewise function - Wikipedia
  2. Master evaluation - To evaluate, simply figure out which sub-function applies to your input, then plug in the value and crunch the numbers. It's like choosing the right recipe from a cookbook based on the dish (interval) you're making. Evaluating Piecewise Functions - Math Hints
  3. Graph with precision - Plot each sub-function only within its designated interval, then use open circles for excluded endpoints and closed ones for included points. This visual roadmap shows exactly how your function behaves across its entire domain. Graphing Piecewise Functions - Pearson
  4. Translate absolute value - Remember that |x| is just a two-part piecewise function: x when x ≥ 0, and - x when x < 0. Seeing absolute value this way makes those tricky equations and inequalities feel like a breeze. Absolute Value as a Piecewise Function - Math Hints
  5. Spot real-world models - From tax brackets and shipping fees to pay-per-piece systems, piecewise functions are everywhere in everyday life. Connecting math to real scenarios makes the concept stick and shows its practical power. Real-World Examples of Piecewise Functions - Math StackExchange
  6. Check continuity - A continuous piecewise function has no pesky jumps or gaps at the boundaries - its sub-functions meet and greet with matching y-values. Ensuring continuity is like making sure two puzzle pieces fit perfectly. Continuity of Piecewise Functions - Math Hints
  7. Reverse-engineer from graphs - Given a graph, identify each line or curve segment and its interval to write down the sub-functions. It's like being a math detective, uncovering the hidden formulas behind the picture. Finding the Formula from a Graph - Online Math Learning
  8. Solve word problems - Translate real-life stories - like tiered pricing for event tickets or income tax calculations - into piecewise expressions. Practicing these applications cements your understanding and shows why piecewise functions rock. Application Problems - Piecewise Functions
  9. Explore step functions - Step functions jump from one constant value to another without in-betweens, modeling situations like digital signals or tiered membership perks. They're your go-to example of piecewise-defined behavior. Step Functions - Pearson
  10. Drill with worksheets - Regular practice through worksheets and problem sets is your secret weapon for mastery. The more you tackle varied examples, the sharper your piecewise-function skills become. Practice Worksheet - Support Worksheet
Make a Quiz (FREE) Copy & Edit This Quiz Create a Quiz with AI

Mathematics Quizzes

Powered by: Quiz Maker