Answer:
- f(x) = 10^x
- f(x) = 7^x
- y > 0
Explanation:
An exponent signifies repeated multiplication.
For example, 10³ = 10·10·10. The exponent 3 means that the base (10) is a factor 3 times in the product.
When you look at the tables in the first two problems, you see that as x increases, the number of times the base (10 or 7) appears in the product increases. This means the variable (x) is an exponent in the function.
Once you realize that, the rest of answer selection has to do with understanding what the answers mean.
1.
- f(x) = -10^x . . . . always produces negative numbers: -1, -10, -100, ...
- f(x) = 10^x . . . . matches the values in the table: 10^0 = 1; 10^1 = 10; ...
- f(x) = 10² . . . . is the constant 100; not a function of x.
- f(x) = 1^x . . . . is the constant 1. x is irrelevant. 1 to any power is 1.
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2. Same as the previous problem, except the base is 7, not 10. The descriptions of answer choices are substantially the same.
f(x) = 7^x
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3. The range of a function has to do with its y-values. The graph shows no values of y below 0, so "all real numbers" is ruled out. The only other choice involving y is the correct one:
y > 0