Piecewise Functions Worksheets Grade 12

1. f(x) = {5x + 10 if x < -5; -x^2 + 20 if -5 ≤ x < 0; 15 if x ≥ 0}. Evaluate f(-6), f(-5), f(-2), f(0), f(5)
2. f(x) = {4x + 8 if x < -4; 2x^2 - 6 if -4 ≤ x < 2; 10 if x ≥ 2}. Evaluate f(-6), f(-4), f(0), f(2), f(6)
3. f(x) = {2x + 7 if x < -2; 3x^2 - 2 if -2 ≤ x < 2; 7x - 2 if x ≥ 2}. Evaluate f(-3), f(-2), f(1), f(2), f(5).

…and 6 more problems

1. Charlotte is a civil engineer designing a new highway overpass. The height of the overpass above the ground, in meters, as a function of horizontal distance x in meters from the start of the structure, is modeled by the piecewise function: h(x) = { 0.5x + 8 for 0 ≤ x < 12; 14 for 12 ≤ x < 20; -0.25x + 19 for 20 ≤ x ≤ 36 } Charlotte needs to verify the design specifications. She must determine the height of the overpass at the points x = 8 meters, x = 12 meters, and x = 28 meters. Additionally, she needs to identify any discontinuities in the height function and describe their type. Finally, she must graph the function for 0 ≤ x ≤ 36. What are the heights h(8), h(12), and h(28), and at what x-value(s) does a discontinuity occur?
2. A pharmaceutical company is modeling the concentration of a new medication in a patient's bloodstream over time. The concentration function is piecewise defined as C(t) = { 2t for 0 ≤ t < 2; 4e^(-0.5(t-2)) for t ≥ 2 }, where t is in hours and C(t) is in mg/L. The medication becomes effective when the concentration first reaches 3 mg/L and remains above this level. Determine the exact time interval during which the medication is effective.
3. Liam is designing a custom skateboard ramp for a competition. The ramp's cross-section is modeled by the piecewise function f(x), where f(x) = 2x + 1 for 0 ≤ x < 2, and f(x) = -x² + 6x - 3 for 2 ≤ x ≤ 5, with x representing horizontal distance in meters and f(x) representing height in meters. At what horizontal distance does the ramp reach its maximum height, and what is that maximum height?

…and 2 more problems

1. Liam is designing a custom skateboard ramp that has a piecewise function for its cross-sectional profile. The ramp's height h(x) in meters at a horizontal distance x meters from the start is defined as: h(x) = { 0.2x² for 0 ≤ x ≤ 3; 1.8 + 0.4(x-3) for 3 < x ≤ 6; 3.0 - 0.1(x-6)² for 6 < x ≤ 9 }. Liam needs to determine the exact horizontal position where the ramp reaches its maximum height. At what x-value does the maximum height occur?
2. f(x) = {5x + 3 if x < -1; -x^2 + 9 if -1 ≤ x < 5; 11 if x ≥ 5}. Evaluate f(-3), f(-1), f(3), f(5), f(7).
3. A pharmaceutical company is modeling the concentration of a new drug in a patient's bloodstream using the piecewise function C(t) = { 2t for 0 ≤ t < 3; 6 + 4e^(-0.5(t-3)) for t ≥ 3 }, where C(t) is the concentration in mg/L and t is time in hours. The drug becomes effective when concentration reaches 5 mg/L and remains effective while concentration stays above 3 mg/L. Determine the total time interval during which the drug is effective.

…and 4 more problems