I am having trouble with functions on a graph. I have a line with the equation y= -1/3+ 6
How do I find the range of the function? For what value of x is f(x)=9? Could someone help me?
The way I think of "range" is the possible values of the y-axis on your graph. The easiest way to see this is to actually enter the function into your graphing calculator and graph it out.
In your example, you have a straight line with a slope of -1/3, so basically it's a diagonal line with values on the y-axis from (-infinity, infinity) because this diagonal line is a ray that stretch to infinity on both ends.
Here's another example. Let's say your equation now is y = 5 (horizontal line). Now your range should be {5} because that's the only possible value on your y-axis. If you get a vertical line such as x = -3, then your range will be (-infinity, infinity).
You wrote << I have a line with the equation
y= -1/3+ 6 >>
That just says that y = 5 2/3
Did you leave out an x somewhere?
Yes I did leave out the x sorry. My equation is y= -1/3x +6.
So is the range supposed to 6 or infinite?
infinite
To find the range of the function, you need to determine the set of all possible values that the output variable (y) can take. In this case, the equation of the line is y = -1/3x + 6.
To find the range, you first need to recognize that this equation represents a straight line with a negative slope (-1/3). The slope tells us that as x increases, y decreases. Since the slope is negative, the line is decreasing from left to right.
The equation is in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. In this case, the y-intercept is 6. This means that when x is 0, y is 6.
To find the range, you need to consider the minimum and maximum y-values the line can have. Since the line is decreasing, the maximum y-value occurs at the y-intercept, which is 6. There is no upper limit to how small y can become since the line extends indefinitely downwards.
So, the range of the function is (-∞, 6], indicating that y can be any value less than or equal to 6.
To find the value of x when f(x) = 9, you need to substitute y = 9 into the equation for y and solve for x.
9 = -1/3x + 6
Subtracting 6 from both sides:
3 = -1/3x
Dividing both sides by -1/3 (or multiplying by -3):
-9 = x
Therefore, when f(x) = 9, the corresponding value of x is -9.