Two big questions that are driving me mad.

1) Given the following linear function sketch the graph of the function and find the domain and range.
f(x) = 2/7x - 2

2) Given the following linear function sketch the graph of the function and find the domain and range.
f(x) = -5x + 4

I really need help on this, I don't understand it at all, and my lesson is no help whatsoever. Answers AND EXPLANATION would be greatly appreciated. :)

think about it. If a line has a nonzero slope, it extends forever, both left-right and down-up.

So, the domain and range are both All Real Numbers.

To sketch the graphs, just pick two values for x, figure the corresponding values for y, plot the two points, and draw the line between them.

Two easy points are the x- and y-intercepts. For the 1st problem,

y = 2/7 x - 2
when x=0, y = -2
when y=0, x = 7

So, plot the points (0,-2) and (7,0) and draw the line that contains them both.

Once you have done that, go back and review your lesson; it might make more sense then.

Sure! I can help you with both of these questions step-by-step.

1) Given the linear function: f(x) = 2/7x - 2

To sketch the graph of this function, we need to plot some points. Let's choose some values for x and calculate the corresponding y-values to create a table of values.

When x = 0, f(x) = 2/7(0) - 2 = -2.
When x = 7, f(x) = 2/7(7) - 2 = 0.
When x = -7, f(x) = 2/7(-7) - 2 = -4.

Plot these points on a graph: (0, -2), (7, 0), and (-7, -4).

Now, draw a straight line through these plotted points. This line represents the graph of the linear function.

To find the domain of the function, we need to determine all possible values for x. In this case, since it is a linear function, the domain is all real numbers (-∞, ∞).

To find the range of the function, we need to determine all possible values for f(x) or y. In this case, the range is also all real numbers (-∞, ∞).

2) Given the linear function: f(x) = -5x + 4

To sketch the graph of this function, we will again create a table of values using different x-values.

When x = 0, f(x) = -5(0) + 4 = 4.
When x = 1, f(x) = -5(1) + 4 = -1.
When x = -1, f(x) = -5(-1) + 4 = 9.

Plot these points on a graph: (0, 4), (1, -1), and (-1, 9).

Draw a straight line through these plotted points. This line represents the graph of the given linear function.

The domain for this function is again all real numbers (-∞, ∞).

The range for this function is also all real numbers (-∞, ∞).

I hope this helps! Let me know if you have any further questions or need additional clarification.

Sure! I can help you with both of these questions and explain the steps along the way to finding the graph, domain, and range.

1) The given linear function is f(x) = (2/7)x - 2.

To sketch the graph:
Step 1: Start by plotting two points on the graph. Choose any two values for x and substitute them into the equation to find their corresponding y-values. For example, if we choose x = 0, we have f(0) = (2/7)(0) - 2 = -2. So one point on the graph is (0, -2). Choose another x-value, such as x = 7. We have f(7) = (2/7)(7) - 2 = 2 - 2 = 0. So another point on the graph is (7, 0).

Step 2: Plot the two points you found on the graph. (0, -2) and (7, 0).

Step 3: Draw a straight line passing through the two plotted points. This line represents the graph of the function.

To find the domain:
The domain of a linear function is all real numbers. In this case, there are no restrictions on the values that x can take. Therefore, the domain is (-∞, +∞) or all real numbers.

To find the range:
The range of a linear function is the set of all possible y-values produced by the function. In this case, since the line continues indefinitely in both positive and negative directions, the range is also all real numbers. So the range is (-∞, +∞) or all real numbers.

2) The given linear function is f(x) = -5x + 4.

To sketch the graph:
Follow the same steps as above to sketch the graph.

Step 1: Plot two points on the graph by choosing x-values and substituting them into the equation to find their corresponding y-values. For example, if x = 0, we have f(0) = -5(0) + 4 = 4. So one point on the graph is (0, 4). Choose another x-value, such as x = 1. We have f(1) = -5(1) + 4 = -5 + 4 = -1. So another point on the graph is (1, -1).

Step 2: Plot the two points (0, 4) and (1, -1) on the graph.

Step 3: Draw a straight line passing through the two plotted points. This line represents the graph of the function.

To find the domain:
Again, the domain of a linear function is all real numbers, so the domain is (-∞, +∞) or all real numbers.

To find the range:
In this case, since the line continues indefinitely in both positive and negative directions, the range is all real numbers. So the range is (-∞, +∞) or all real numbers.

I hope this explanation helps you understand how to sketch the graph and find the domain and range of linear functions. Let me know if you have any further questions!