1. Make a table of values for y = 2x, y= 3x and y=0.5x
2. Graph all three functions on the same set of axes.
3. For each function, describe key properties relating to domain, range, intercepts, increasing/decreasing intervals, and asymptotes.
4. Make comparisons between the graphs, and explain the relationship between the y-intercepts.
2. Graph all three functions on the same set of axes.
3. For each function, describe key properties relating to domain, range, intercepts, increasing/decreasing intervals, and asymptotes.
4. Make comparisons between the graphs, and explain the relationship between the y-intercepts.
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(These should be y = 2^x, y = 3^x, and y = 0.5^x.)
For the tables of values, simply choose a few values for x, such as -2, -1, 0, 1, 2, and compute the corresponding y-values.
All simple exponential functions -- those of the form y = a^x, rather than more complex functions such as y = a^x - 3, or y = a^x + x^2, etc. -- have the following properties:
* Their domain is (-∞, +∞).
* Their range is (0, +∞).
* The y-intercept for each such function is the point (0,1).
* Their graphs are strictly increasing; no level regions or decreases anywhere.
* They have the x-axis as a horizontal asymptote; they have no vertical asymptote.
All the y-intercepts are the same, because for every function y = a^x, x = 0 means
y = a^0 = 1.
For the tables of values, simply choose a few values for x, such as -2, -1, 0, 1, 2, and compute the corresponding y-values.
All simple exponential functions -- those of the form y = a^x, rather than more complex functions such as y = a^x - 3, or y = a^x + x^2, etc. -- have the following properties:
* Their domain is (-∞, +∞).
* Their range is (0, +∞).
* The y-intercept for each such function is the point (0,1).
* Their graphs are strictly increasing; no level regions or decreases anywhere.
* They have the x-axis as a horizontal asymptote; they have no vertical asymptote.
All the y-intercepts are the same, because for every function y = a^x, x = 0 means
y = a^0 = 1.
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its 3 straight lines
just different angles of inclination
domain=all real
range=all real
intercept=0
idk how this is hard..unless u wrote this question wrong
just different angles of inclination
domain=all real
range=all real
intercept=0
idk how this is hard..unless u wrote this question wrong