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Some Functions & their Graphs Video Lecture | Mathematics (Maths) Class 11 - Commerce

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FAQs on Some Functions & their Graphs Video Lecture - Mathematics (Maths) Class 11 - Commerce

1. What are some common examples of functions and their corresponding graphs?
Ans. Some common examples of functions and their corresponding graphs include linear functions, quadratic functions, exponential functions, logarithmic functions, and trigonometric functions. Linear functions have a straight line graph, quadratic functions have a parabolic graph, exponential functions have a curved graph that increases or decreases rapidly, logarithmic functions have a graph that increases or decreases slowly, and trigonometric functions have periodic graphs such as sine and cosine waves.
2. How can I determine the domain and range of a function from its graph?
Ans. To determine the domain of a function from its graph, we look at the x-values that are included or excluded on the graph. The domain is the set of all possible x-values for which the function is defined. Similarly, to determine the range of a function from its graph, we look at the y-values that are included or excluded on the graph. The range is the set of all possible y-values that the function can output.
3. What does the slope of a linear function represent on its graph?
Ans. The slope of a linear function represents the rate of change of the function. It tells us how much the y-value changes for a given change in the x-value. A positive slope indicates an increasing function, while a negative slope indicates a decreasing function. A slope of zero represents a horizontal line with no change in the y-value regardless of the x-value.
4. How can I determine the x-intercepts and y-intercepts of a function from its graph?
Ans. To determine the x-intercepts of a function from its graph, we look for the points where the graph intersects the x-axis. These points have a y-coordinate of zero, and their corresponding x-coordinate gives us the x-intercepts. Similarly, to determine the y-intercepts of a function from its graph, we look for the points where the graph intersects the y-axis. These points have an x-coordinate of zero, and their corresponding y-coordinate gives us the y-intercepts.
5. How can I identify the symmetry of a function's graph?
Ans. The symmetry of a function's graph can be identified through its equation or by analyzing the graph itself. A function is symmetric with respect to the y-axis if replacing x with -x in the equation does not change the function. This means that the graph is reflectionally symmetric, and any point (x, y) on the graph should have the point (-x, y) as well. On the other hand, a function is symmetric with respect to the x-axis if replacing y with -y in the equation does not change the function. This means that the graph is symmetric about the x-axis, and any point (x, y) on the graph should have the point (x, -y) as well.
75 videos|238 docs|91 tests

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