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More in Functions and Calculus
Sets and Intervals
Relations and Functions
Graphs of Functions
Composite and Inverse Functions
Functions as Models of Data
Functional Equations
Counting Functions
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16 problems
Type:
Any
Conceptual
Numerical
1.
Write f(x) = (x - 2)³ as the sum of an even function and an odd function.
High School (11–12) · Graphs of Functions
StemPy Lab
Hard
2.
Show that {x} = x - [x] has period 1. Then find the period of {5x}.
High School (11–12) · Graphs of Functions
StemPy Lab
Medium
3.
For f(x) = -x² + 10x, find the interval on which f is increasing, the interval on which it is…
High School (11–12) · Graphs of Functions
StemPy Lab
Medium
4.
Say whether each function is even, odd or neither. 1/x³; x⁴ + x²; x² + x; x|x|
High School (11–12) · Graphs of Functions
StemPy Lab
Easy
5.
Describe the graph of y = 1/(x + 1) - 2. Give the asymptotes, the domain and the range.
High School (11–12) · Graphs of Functions
StemPy Lab
Medium
6.
Describe how to get the graph of y = √(9 - x) from the graph of y = √x.
High School (11–12) · Graphs of Functions
StemPy Lab
Hard
7.
The point (3, 4) is on the graph of y = f(x).
High School (11–12) · Graphs of Functions
StemPy Lab
Medium
8.
Describe how to get the graph of y = -3(x + 2)² + 4 from the graph of y = x².
High School (11–12) · Graphs of Functions
StemPy Lab
Medium
9.
Write f(x) = |x + 2| + |x - 3| without bars for (a) x < -2, (b) -2 ≤ x ≤ 3 and (c) x > 3.
High School (11–12) · Graphs of Functions
StemPy Lab
Hard
10.
Solve (a) |3x + 1| < 8 and (b) |x - 2| ≥ 5.
High School (11–12) · Graphs of Functions
StemPy Lab
Medium
11.
A function is defined by f(x) = 2x + 1, x < 0; x², 0 ≤ x ≤ 3; 12 - x, x > 3.
High School (11–12) · Graphs of Functions
StemPy Lab
Medium
12.
Find [x] and {x} = x - [x] for x = 6.2, -3.6, 4 and -0.25.
High School (11–12) · Graphs of Functions
StemPy Lab
Easy
13.
For which value of k does the graph of y = x² - 10x + k touch the x-axis at exactly one point?
High School (11–12) · Graphs of Functions
StemPy Lab
Medium
14.
A ball is thrown straight up. After t seconds its height is h = 30t - 5t² metres.
High School (11–12) · Graphs of Functions
StemPy Lab
Medium
15.
Find f(x) = 1/x² for x = 0.2, 0.02, 20 and -20.
High School (11–12) · Graphs of Functions
StemPy Lab
Easy
16.
For y = -x² + 4x + 12, find the vertex, the zeros, the y-intercept and the range.
High School (11–12) · Graphs of Functions
StemPy Lab
Easy
StemPy Lab