ab^x+k=y
1.) if a<0 is y<0 always is y>0 always or is y<0 sometimes
2.) if a>0 is y<0 always is y>0 always or is y<0 sometimes
DO SAME PROCEDURE FOR BOTH A B AND K
exponental functions and ranges?
2017-02-14 1:43 pm
回答 (1)
2017-02-14 2:30 pm
b^x will have a range of (0, ∞) for positive b. For negative b, it will only have real values for integer x, but those values can range over (-∞, ∞). Thus, depending on the value of k, the value of y may or may not have the same sign as "a". "sometimes" seems the appropriate choice in both cases.
The graph shows a case where y changes sign (so is sometimes negative) for each of your conditions above.
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Knowing that b^x is always positive (for positive b), you can adjust "a" and "k" to make "y" have whatever sign you want. That is, if "a" and "k" have the same sign, "y" will "always" have that sign.
If "b" is negative, there will be some set of integer values of x that will cause y to alternate signs for consecutive integers, regardless of the values of "a" and "k".
The graph shows a case where y changes sign (so is sometimes negative) for each of your conditions above.
_____
Knowing that b^x is always positive (for positive b), you can adjust "a" and "k" to make "y" have whatever sign you want. That is, if "a" and "k" have the same sign, "y" will "always" have that sign.
If "b" is negative, there will be some set of integer values of x that will cause y to alternate signs for consecutive integers, regardless of the values of "a" and "k".
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