Find the first four terms of the sequence represented by the expression.
3n + 5
When n = 1: 3(1) + 5 = 8
When n = 2: 3(2) + 5 = 11
When n = 3: 3(3) + 5 = 14
When n = 4: 3(4) + 5 = 17
Therefore, the first four terms of the sequence represented by the expression 3n + 5 are 8, 11, 14, and 17.
which is a table of values for y=x -6
Here is a table of values for y = x - 6:
|x | y |
|- | - |
|0 | -6|
|1 | -5|
|2 | -4|
|3 | -3|
|4 | -2|
|5 | -1|
|6 | 0 |
|7 | 1 |
|8 | 2 |
|9 | 3 |
In this table, we can see that when x = 0, y = -6. As x increases by 1, y increases by 1. This is because the expression y = x - 6 represents a line with a slope of 1 and a y-intercept of -6.
i still dont get it
No problem, let me try to explain in simpler terms.
The equation y = x - 6 means that we take any value of x and subtract 6 from it to get the corresponding value of y. For example, if x is 3, then y would be 3 - 6 = -3.
To create a table of values, we choose several values of x and calculate the corresponding values of y. In the table I provided before, we chose x to be 0, 1, 2, 3, and so on, up to 9. We then subtracted 6 from each of these x values to get the corresponding y values.
For example, when x is 0, we have y = 0 - 6 = -6. Similarly, when x is 1, we have y = 1 - 6 = -5. When x is 2, we have y = 2 - 6 = -4, and so on.
In this way, we can create a table that shows the values of both x and y. We can then use this table to plot the points and draw a line that represents the equation y = x - 6. I hope this explanation is clearer for you!
what is function notation
Function notation is a way of writing a function using symbols and variables. It is used to describe a relation between two variables, where the value of one variable is determined by the value of the other variable.
Function notation uses the symbol "f" to represent a function, and an input or independent variable is represented by the symbol "x". The output or dependent variable is represented by "f(x)".
For example, if we have a function f(x) = 2x + 3, we can input different values of x and find the corresponding output. If we input x = 2, then f(2) = 2(2) + 3 = 7. If x = 4, then f(4) = 2(4) + 3 = 11.
In this way, function notation allows us to generalize a rule that relates x and y into a symbolically simpler expression. It is widely used in mathematics to model real-world situations and to solve problems by setting up equations representing a function.
Use the function rule f(x) = 3x - 2.
We can use the function rule f(x) = 3x - 2 to find the corresponding output for any input value of x.
For example, if x = 0, then f(0) = 3(0) - 2 = -2. This means that when x is 0, the output is -2.
Similarly, if x = 1, then f(1) = 3(1) - 2 = 1. This means that when x is 1, the output is 1.
We can also create a table of values for this function to help us see the pattern of the input and output values.
| x | f(x) |
|---|------|
| 0 | -2 |
| 1 | 1 |
| 2 | 4 |
| 3 | 7 |
| 4 | 10 |
In this table, we can see that as x increases by 1, the output value f(x) increases by 3. This is because the function rule tells us that for any value of x, the output is 3 times x minus 2.