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Evaluating Piecewise Functions — Easy Worksheet 2
Grade 12 · MathSheets Name: ____________________ Date: __________
Evaluate the function at the given value of x.
How to solve
Compare the given x-value with each condition to choose the correct piece. Substitute x into only that piece and simplify.
Example
f(x) = -x - 3 if x < 4; f(x) = 2x + 2 if x ≥ 4. Find f(1).
Answer: -4
Not quite. The answer is
💡 4 ≥ 2, so use the second piece, f(x) = 3x − 3. Substitute: f(4) = 3(4) − 3 = 12 − 3 = 9. So f(4) = 9.
✓ Correct!
Not quite. The answer is
💡 4 ≥ 2, so use the second piece, f(x) = 3x − 3. Substitute: f(4) = 3(4) − 3 = 12 − 3 = 9. So f(4) = 9.
💡 How to solve: Evaluating Piecewise Functions
Compare the given x-value with each condition to choose the correct piece. Substitute x into only that piece and simplify.
Try a similar one
f(x) = 2x + 2 if x < 0; f(x) = x if x ≥ 0. Find f(-2).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 −7 < −4, so use the first piece, f(x) = 2x. Substitute: f(−7) = 2(−7) = −14. So f(−7) = −14.
✓ Correct!
Not quite. The answer is
💡 −7 < −4, so use the first piece, f(x) = 2x. Substitute: f(−7) = 2(−7) = −14. So f(−7) = −14.
💡 How to solve: Evaluating Piecewise Functions
Compare the given x-value with each condition to choose the correct piece. Substitute x into only that piece and simplify.
Try a similar one
f(x) = 2x + 2 if x < -4; f(x) = -x + 3 if x ≥ -4. Find f(-6).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 −3 ≥ −4, so use the second piece, f(x) = 3x + 3. Substitute: f(−3) = 3(−3) + 3 = −9 + 3 = −6. So f(−3) = −6.
✓ Correct!
Not quite. The answer is
💡 −3 ≥ −4, so use the second piece, f(x) = 3x + 3. Substitute: f(−3) = 3(−3) + 3 = −9 + 3 = −6. So f(−3) = −6.
💡 How to solve: Evaluating Piecewise Functions
Compare the given x-value with each condition to choose the correct piece. Substitute x into only that piece and simplify.
Try a similar one
f(x) = x - 2 if x < -5; f(x) = -x - 4 if x ≥ -5. Find f(-1).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 2 ≥ −1, so use the second piece, f(x) = −3x + 3. Substitute: f(2) = −3(2) + 3 = −6 + 3 = −3. So f(2) = −3.
✓ Correct!
Not quite. The answer is
💡 2 ≥ −1, so use the second piece, f(x) = −3x + 3. Substitute: f(2) = −3(2) + 3 = −6 + 3 = −3. So f(2) = −3.
💡 How to solve: Evaluating Piecewise Functions
Compare the given x-value with each condition to choose the correct piece. Substitute x into only that piece and simplify.
Try a similar one
f(x) = -4x - 4 if x < 2; f(x) = 3x - 4 if x ≥ 2. Find f(-2).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 0 ≥ −3, so use the second piece, f(x) = 2x − 2. Substitute: f(0) = 2(0) − 2 = 0 − 2 = −2. So f(0) = −2.
✓ Correct!
Not quite. The answer is
💡 0 ≥ −3, so use the second piece, f(x) = 2x − 2. Substitute: f(0) = 2(0) − 2 = 0 − 2 = −2. So f(0) = −2.
💡 How to solve: Evaluating Piecewise Functions
Compare the given x-value with each condition to choose the correct piece. Substitute x into only that piece and simplify.
Try a similar one
f(x) = 3x + 2 if x < 1; f(x) = -4x - 2 if x ≥ 1. Find f(-1).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 1 < 2, so use the first piece, f(x) = 3x + 3. Substitute: f(1) = 3(1) + 3 = 3 + 3 = 6. So f(1) = 6.
✓ Correct!
Not quite. The answer is
💡 1 < 2, so use the first piece, f(x) = 3x + 3. Substitute: f(1) = 3(1) + 3 = 3 + 3 = 6. So f(1) = 6.
💡 How to solve: Evaluating Piecewise Functions
Compare the given x-value with each condition to choose the correct piece. Substitute x into only that piece and simplify.
Try a similar one
f(x) = 2x if x < 2; f(x) = x + 1 if x ≥ 2. Find f(0).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 −4 < 1, so use the first piece, f(x) = −x − 2. Substitute: f(−4) = −(−4) − 2 = 4 − 2 = 2. So f(−4) = 2.
✓ Correct!
Not quite. The answer is
💡 −4 < 1, so use the first piece, f(x) = −x − 2. Substitute: f(−4) = −(−4) − 2 = 4 − 2 = 2. So f(−4) = 2.
💡 How to solve: Evaluating Piecewise Functions
Compare the given x-value with each condition to choose the correct piece. Substitute x into only that piece and simplify.
Try a similar one
f(x) = -4x + 1 if x < 0; f(x) = -3x if x ≥ 0. Find f(4).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 −2 ≥ −4, so use the second piece, f(x) = −2x + 4. Substitute: f(−2) = −2(−2) + 4 = 4 + 4 = 8. So f(−2) = 8.
✓ Correct!
Not quite. The answer is
💡 −2 ≥ −4, so use the second piece, f(x) = −2x + 4. Substitute: f(−2) = −2(−2) + 4 = 4 + 4 = 8. So f(−2) = 8.
💡 How to solve: Evaluating Piecewise Functions
Compare the given x-value with each condition to choose the correct piece. Substitute x into only that piece and simplify.
Try a similar one
f(x) = -4x - 3 if x < -5; f(x) = -x + 4 if x ≥ -5. Find f(-5).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Evaluating Piecewise Functions — Easy Worksheet 2
Evaluate the function at the given value of x.