Engineering Mathematics Exam > Engineering Mathematics Videos > How to match function input to output given the graph (example) - Algebra I, Mathematics
How to match function input to output given the graph (example) - Algebra I, Mathematics Video Lecture - Engineering Mathematics
FAQs on How to match function input to output given the graph (example) - Algebra I, Mathematics Video Lecture - Engineering Mathematics
| 1. How can I match a function's input to its output using a graph? |  |
Ans. To match a function's input to its output using a graph, you need to identify the x-values (inputs) on the graph and then find the corresponding y-values (outputs) on the graph. The x-values are usually shown on the horizontal axis, and the y-values are shown on the vertical axis. By locating a point on the graph, you can determine the input-output relationship for that specific point.
| 2. What does the slope of a graph represent in terms of input and output? | |
Ans. The slope of a graph represents the rate of change between the input and output variables. It shows how the output changes for every unit increase in the input. A positive slope indicates an increasing relationship, where the output values increase as the input values increase. Conversely, a negative slope represents a decreasing relationship, where the output values decrease as the input values increase.
| 3. How do I determine the domain and range of a function from its graph? | |
Ans. To determine the domain and range of a function from its graph, you need to examine the x-values and y-values shown on the graph. The domain is the set of all possible input values, which can be found by looking at the x-values shown on the graph. The range, on the other hand, is the set of all possible output values, which can be determined by looking at the y-values shown on the graph.
| 4. Can I determine if a function is one-to-one from its graph? | |
Ans. Yes, you can determine if a function is one-to-one by analyzing its graph. A function is considered one-to-one if each input value corresponds to a unique output value, and no two different input values produce the same output value. On a graph, this means that a horizontal line should intersect the graph at most once. If there are any horizontal lines that intersect the graph at multiple points, then the function is not one-to-one.
| 5. How can I use a graph to identify the maximum or minimum values of a function? | |
Ans. To identify the maximum or minimum values of a function using a graph, you need to look for the highest or lowest point on the graph, respectively. For maximum values, locate the highest point (vertex) on an upward-opening graph or the lowest point on a downward-opening graph. For minimum values, locate the lowest point (vertex) on an upward-opening graph or the highest point on a downward-opening graph. These points represent the maximum or minimum values of the function, respectively.
Text Transcript from Video
The graph of the function g is shown below
What is the input value for which g of x
is equal to negative 2?
So what they do here is along the x axis
these are the inputs and then the graph
shows us what's the output
so when x is equal to 7,
G of 7 we see here is 1.
If x equals 9,
g of 9 here is 2.
If x equals 6,
g of 6 is equal to the y coordinate at
this point is equal to 0.
so what is the input value for which g is
equal to negative 2?
so this graph over here, this is y equals
g of x.
So g of x equaling to negative 2 means y
of x is equal to negative 2
And so when does y equal negative 2?
(muttering) when does equal negative 2?
(talking) it looks like that happens right
at this point.
And that happens when you input negative 9
into g.
g of negative 9 is negative 2
so this is going to be negative 9.
And we're done.
What is the input value for which g of x
is equal to negative 2?
So what they do here is along the x axis
these are the inputs and then the graph
shows us what's the output
so when x is equal to 7,
G of 7 we see here is 1.
If x equals 9,
g of 9 here is 2.
If x equals 6,
g of 6 is equal to the y coordinate at
this point is equal to 0.
so what is the input value for which g is
equal to negative 2?
so this graph over here, this is y equals
g of x.
So g of x equaling to negative 2 means y
of x is equal to negative 2
And so when does y equal negative 2?
(muttering) when does equal negative 2?
(talking) it looks like that happens right
at this point.
And that happens when you input negative 9
into g.
g of negative 9 is negative 2
so this is going to be negative 9.
And we're done.
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Nov 18, 2024 Last updated |
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