Mathematics
Grade 11
15 min
Find values using function graphs
Find values using function graphs
What you'll learn
- Identify the hour and minute hands on at least 8 out of 10 different analog clocks.
- Match at least 7 out of 10 analog clocks to their corresponding digital times (e.g., 3:30) correctly.
- Explain in their own words how to tell time to the half-hour (e.g., 'The big hand points to the 6 and the little hand is halfway between the numbers.')
- Draw the hands on at least 3 out of 5 blank clock faces to show a given time to the half-hour (e.g., draw the hands to show 7:30).
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Evaluate a function for a specific input value using its graph (e.g., find f(a)).
Find the input value(s) for a given function output using its graph (e.g., solve f(x) = b).
Determine the domain and range of a function from its graphical representation.
Identify the x-intercepts (zeros) and the y-intercept of a function from its graph.
Solve equations and inequalities involving one or two functions by analyzing their graphs (e.g., f(x) = g(x) or f(x) > c).
Evaluate composite functions using their graphs (e.g., find f(g(2))).
Interpret the meaning of function values in the context of a real-world problem represented by a graph.
How can a stock market analyst predict trends or a physicist track a particle's movement without a single equation? 📈 T...
2
Key Concepts & Vocabulary
TermDefinitionExample
Function EvaluationThe process of finding the output value of a function, f(x), that corresponds to a specific input value, x. On a graph, this means finding the y-coordinate for a given x-coordinate.If the point (2, 7) is on the graph of f(x), then evaluating the function at x=2 gives f(2) = 7.
DomainThe complete set of all possible input values (x-values) for which the function is defined. Graphically, it is the horizontal extent of the graph.For a graph that starts at x = -5 and ends at x = 3, the domain is the interval [-5, 3].
RangeThe complete set of all possible output values (y-values) that the function can produce. Graphically, it is the vertical extent of the graph.For a parabola with its lowest point at y = -4, the range is [-4, ∞).
x-intercept (Zero)A poi...
3
Core Formulas
Finding an Output Value
To find f(a), find x = a on the horizontal axis, move vertically (up or down) to the graph, then move horizontally to the vertical axis to read the corresponding y-value.
This is the fundamental process for evaluating a function at a specific point using its graph. It answers the question, 'What is the output for this input?'
Finding Input Value(s)
To solve f(x) = b, find y = b on the vertical axis, move horizontally (left or right) to the graph, then move vertically to the horizontal axis to read the corresponding x-value(s).
This process is used to find the input(s) that result in a specific output. Note that there can be one, more than one, or no solutions.
Solving f(x) = g(x)
The solutions to the equation f(x) = g(x) are the x-coor...
4 more steps in this tutorial
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Challenging
The graph of y = f(x) is a parabola with vertex at (2, 5) passing through (0, 1). The graph of y = g(x) is a line passing through (1, 2) and (5, 0). What is the value of f(g(5))?
A.1
B.5
C.0
D.2
Challenging
The graph of f(x) = x² (a parabola with vertex at (0,0)) and g(x) = x + 2 (a line) are shown. How many solutions does the equation f(x) = g(x) - 3 have?
A.0
B.1
C.2
D.Cannot be determined
Challenging
The graph of a continuous function y = h(x) has a local maximum at (-2, 7) and a local minimum at (4, -1). For which value of k will the equation h(x) = k have exactly three distinct real solutions?
A.k = 8
B.k = 7
C.k = -1
D.k = 3
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Frequently asked questions
What grade level is "Find values using function graphs"?
Find values using function graphs is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Find values using function graphs?
You'll be able to: Identify the hour and minute hands on at least 8 out of 10 different analog clocks; Match at least 7 out of 10 analog clocks to their corresponding digital times (e.g., 3:30) correctly; Explain in their own words how to tell….
Is "Find values using function graphs" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Find values using function graphs?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.