Answer:
f(x)=50x
Step-by-step explanation:
f(x)= y
y= 50
if x is 1 the answer is 50
if x is 2 the answer is 100
The numbers will just keep getting higher depending on the x value
Answer:
8/17
Step-by-step explanation:
opposite = hypotenuse
opposite = 8
hypotenuse =17
1. We use the recursive formula to make the table of values:
f(1) = 35
f(2) = f(1) + f(2-1) = f(1) + f(1) = 35 + 35 = 70
f(3) = f(1) + f(3-1) = f(1) + f(2) = 35 + 70 = 105
f(4) = f(1) + f(4-1) = f(1) + f(3) = 35 + 105 = 140
f(5) = f(1) + f(5-1) = f(1) + f(4) = 35 + 140 = 175
2. We observe that the pattern is that for each increase of n by 1, the value of f(n) increases by 35. The explicit equation would be that f(n) = 35n. This fits with the description that Bill saves up $35 each week, thus meaning that he adds $35 to the previous week's value.
3. Therefore, the value of f(40) = 35*40 = 1400. This is easier than having to calculate each value from f(1) up to f(39) individually. The answer of 1400 means that Bill will have saved up $1400 after 40 weeks.
4. For the sequence of 5, 6, 8, 11, 15, 20, 26, 33, 41...
The first-order differences between each pair of terms is: 1, 2, 3, 4, 5, 6, 7, 8...since these differences form a linear equation, this sequence can be expressed as a quadratic equation. Since quadratics are functions (they do not have repeating values of the x-coordinate), therefore, this sequence can also be considered a function.
The equation for the vertical translation of y=f(x). 2 units up is y=f(x)+2.
Using equations of the form y=f(x), you may be able to modify the graph in various ways. For example, you can move the chart up, down, left, or right, flip it around the x or y-axis, or stretch or shrink it vertically or horizontally. Understanding these transformations makes it easy to graph different functions. Start with a "basic model" and apply a series of transformations/modifications to change it to the desired function.
A point on the graph of y=f(x) has the shape (x,f(x)).
The points on the graph of y=f(x)+2 are of the form (x,f(x)+2).
So, the graph for y=f(x) +2 is the same as the graph for y=f(x) shifted up by 2 units.
The new equation is:
y=f(x)+2
More problems related to the translation of shapes are given below.
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