Answer:
- a) 3
- b) 6
- c) 9
- d) the outputs are 3 times as far apart as the inputs
Step-by-step explanation:
(a) "x" in considered to be the input to the function f(x). The variable(s) in parentheses as part of the function name are the inputs. The function value itself is the output.
That is, for an input (x-value) of 0, the output (f(0)) is 5. For an input of 1, the output (f(1)) is 8. These input values (0 and 1) are 1 unit apart: 1 - 0 = 1. The corresponding output values are 3 units apart: 8 - 5 = 3.
(b) Inputs -1 and 1 are 2 units apart (1-(-1)=2). The corresponding output values, 2 and 8, are 6 units apart. (8-2=6)
(c) Inputs 0 and 3 are 3 units apart. The corresponding output values, 5 and 14, are 9 units apart.
(d) The ratio of output differences to input differences can be seen to be ...
... 3/1 = 6/2 = 9/3 = 3
Output differences are 3 times input differences.
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<em>Comment on the problem</em>
These ratios are constant everywhere, so the function is considered to be "linear." The ratio is the "slope" of the line you see when the function is graphed.
Answer:
- g(20) > f(20)
- g(x) exceeds f(x) for any x > 4
Step-by-step explanation:
As with most graphing problems not involving straight lines, it works well to start with a table of values. Pick a few values of x and compute f(x) and g(x) for those values. Plot the points and draw a smooth curve through them.
As in the attached, your table will show that there are two points of intersection between f(x) and g(x), and that for values of x more than 4, g(x) becomes much greater very quickly. Both curves rapidly reach the top of your graph space.
To find whether f(20) or g(20) is greater, you can evaluate the functions for that value of x.
f(20) = 20² = 400
g(20) = 2²⁰ = 1,048,576
Clearly, g(20) has a greater value.
Answer:
10n - 7
Step-by-step explanation:
Choose a variable for the number
let "n" be the number
Take apart the statement in the question. Convert each part to algebraic form (numbers and symbols)
"Seven less than" -7
"the product of a number and 10" n*10 or 10n
Put the parts together
10n - 7
This is an expression, which means there is no equal sign. When there is an equal sign, it's an equation.
You cannot solve an expression, unless given the missing number.
We are adding 7 each time.
The formula for an arithmetic sequence is
first term+(n-1)d
Where n is the number of terms, and d is the common difference
In this case, n is 35 and d is 7
Plug the numbers into the formula and you get
-33+(35-1)7
Solve
-33+(238)= 205
Answer:
each song is .99
Step-by-step explanation:
3.96/4
Price/song