1. Determine whether the relation is a function.
{(-2, -7), (3, -5), (6, -4), (9, -6), (10, -1)}
2. Determine whether the relation is a function.
{(-5, -4), (-2, 9), (-1, -2), (-1, 7)}
3. Determine whether the relation is a function.
{(-7, -1), (-7, 2), (-1, 8), (3, 3), (10, -7)}
4. Determine whether the relation is a function.
{(1, -3), (1, 1), (6, -8), (9, -3), (11, -3)}
5. Determine whether the relation is a function.
{(-6, -9), (-2, 1), (1, -1), (7, -7)}
6. Determine whether the equation defines y as a function of x.
x + y = 9
7. Determine whether the equation defines y as a function of x.
x2 + y2 = 1
8. Determine whether the equation defines y as a function of x.
x = y2
9. Evaluate the function at the given value of the independent variable and simplify.
f(x) = -3x - 8; f(-2)
10. Evaluate the function at the given value of the independent variable and simplify.
f(x) = x2 - 1; f(x - 2)
11. Evaluate the function at the given value of the independent variable and simplify.
f(x) = 4x2 + 5x - 6; f(x - 1)
12. Evaluate the function at the given value of the independent variable and simplify.
f(x) = ; f(5)
13. Find the slope of the line that goes through the given points.
(3, -5), (-9, -8)
14. Find the slope of the line that goes through the given points.
(-7, 6), (-7, -9)
15. Find the slope of the line that goes through the given points.
(-1, 4), (5, 4)
16. Find the slope of the line that goes through the given points.
(-2, -6), (-9, -17)
17. Find the slope of the line that goes through the given points.
(-8, 8), (-5, 2)
18. Find the slope of the line that goes through the given points.
(-3, -7), (9, -7)
19. Use the given conditions to write an equation for the line in point-slope form.
Slope = 4, passing through (-3, 7)
20. Use the given conditions to write an equation for the line in point-slope form.
Slope = , passing through (8, 7)
Wow, looks like "homework dumping" to me
1. Yes, it is a function, but it's not a very sociable one. It only has one friend for each x value. It's not the life of the party, that's for sure.
2. No, this relation is not a function. It's like having multiple people with the same name at a party - it just gets confusing.
3. No, this relation is not a function either. It's like having two people with the same phone number - how do you know who you're talking to?
4. No, this relation is not a function. It's like having multiple people with the same address - mail would get mixed up all the time.
5. Yes, this relation is a function. Each x-value has only one corresponding y-value. It's a relationship built on trust and reliability.
6. Yes, this equation defines y as a function of x. In this case, y depends on x, but x doesn't depend on y. It's like saying, "You have to come to the party, but I won't come if you're there."
7. No, this equation does not define y as a function of x. It's more like a love-hate relationship. Both x and y have their own rules and don't depend on each other.
8. No, this equation does not define y as a function of x. It's like saying, "You can only come to the party if you're lucky enough to be my square."
9. Simplifying the function f(x) = -3x - 8 and evaluating it at f(-2), we get f(-2) = -3(-2) - 8 = 6 - 8 = -2. So, f(-2) = -2. The function is like a grumpy teenager - it doesn't like negative numbers.
10. Simplifying the function f(x) = (x-2)^2 - 1 and evaluating it at f(x-2), we get f(x-2) = (x-2-2)^2 - 1 = (x-4)^2 - 1. So, f(x-2) = (x-4)^2 - 1. The function is like a roller coaster - it takes you on a wild ride by shifting the x-coordinate.
11. Simplifying the function f(x) = 4(x-1)^2 + 5(x-1) - 6 and evaluating it at f(x-1), we get f(x-1) = 4(x-1-1)^2 + 5(x-1-1) - 6 = 4(x-2)^2 + 5(x-2) - 6. So, f(x-1) = 4(x-2)^2 + 5(x-2) - 6. The function is like a contortionist - it twists and turns the x-coordinate.
12. Sorry, but there is no given function to evaluate at f(5). It's like trying to find something in an empty refrigerator - there's nothing there.
13. The slope of the line between (3, -5) and (-9, -8) is -3/4. The line is going downhill, and it's not inviting to skiers or snowboarders.
14. The slope of the line between (-7, 6) and (-7, -9) is undefined. It's like trying to go up and down on an escalator that's not moving.
15. The slope of the line between (-1, 4) and (5, 4) is 0. It's as flat as a pancake - no exciting roller coaster rides here.
16. The slope of the line between (-2, -6) and (-9, -17) is 11/7. It's like going up a moderate hiking trail - a little steep, but doable.
17. The slope of the line between (-8, 8) and (-5, 2) is -2. It's like sliding down a slippery slope - watch out for falling.
18. The slope of the line between (-3, -7) and (9, -7) is 0. It's like walking on a level surface - no need to climb or descend.
19. The equation of the line with slope 4 passing through (-3, 7) can be written in point-slope form as y - 7 = 4(x - (-3)). Simplifying, we get y - 7 = 4(x + 3), or y - 7 = 4x + 12. This line is like a cheerleader - it's always on the up and up.
20. Sorry, but you forgot to give the slope for the line passing through (8, 7), so we can't write an equation in point-slope form. It's like trying to knit a sweater without any yarn - it's just not going to happen.
1. To determine if a relation is a function, we need to check if each input value (x) is paired with only one output value (y). In this case, the relation is a function because each x-coordinate is paired with only one y-coordinate.
2. To determine if a relation is a function, we need to check if each input value (x) is paired with only one output value (y). In this case, the relation is not a function because the input value -1 is paired with both -2 and 7.
3. To determine if a relation is a function, we need to check if each input value (x) is paired with only one output value (y). In this case, the relation is not a function because the input value -7 is paired with both -1 and 2.
4. To determine if a relation is a function, we need to check if each input value (x) is paired with only one output value (y). In this case, the relation is not a function because the input value 1 is paired with multiple output values (-3, 1, -3).
5. To determine if a relation is a function, we need to check if each input value (x) is paired with only one output value (y). In this case, the relation is a function because each x-coordinate is paired with only one y-coordinate.
6. To determine if the equation defines y as a function of x, we need to solve the equation for y. In this case, the equation x + y = 9 can be rewritten as y = 9 - x. Since we can express y in terms of x, the equation defines y as a function of x.
7. To determine if the equation defines y as a function of x, we need to solve the equation for y. In this case, the equation x^2 + y^2 = 1 cannot be rewritten as y = f(x) because it is an equation of a circle. Therefore, the equation does not define y as a function of x.
8. To determine if the equation defines y as a function of x, we need to solve the equation for y. In this case, the equation x = y^2 can be rewritten as y = ±√x. Since for each x-value there are two possible y-values, the equation does not define y as a function of x.
9. To evaluate the function at the given value of the independent variable (-2), we substitute the value of x into the function f(x) = -3x - 8. Therefore, f(-2) = -3(-2) - 8 = 6 - 8 = -2.
10. To evaluate the function at the given value of the independent variable (x - 2), we plug in the expression (x - 2) into the function f(x) = x^2 - 1. Therefore, f(x - 2) = (x - 2)^2 - 1.
11. To evaluate the function at the given value of the independent variable (x - 1), we substitute the value of (x - 1) into the function f(x) = 4x^2 + 5x - 6. Therefore, f(x - 1) = 4(x - 1)^2 + 5(x - 1) - 6.
12. The function f(x) = does not provide any equation or expression to evaluate for a specific value.
13. To find the slope of the line, we use the formula: slope = (y2 - y1) / (x2 - x1). In this case, the coordinates of the two points are (3, -5) and (-9, -8). Thus, the slope = (-8 - (-5)) / (-9 - 3) = -3 / -12 = 1/4.
14. The given points (-7, 6) and (-7, -9) have the same x-coordinate but different y-coordinates. For this type of situation, the slope is undefined because the line is vertical.
15. The given points (-1, 4) and (5, 4) have the same y-coordinate but different x-coordinates. For this type of situation, the slope is 0.
16. To find the slope of the line passing through the given points (-2, -6) and (-9, -17), we use the formula: slope = (y2 - y1) / (x2 - x1). By substituting the coordinates, we get slope = (-17 - (-6)) / (-9 - (-2)) = -11 / -7 = 11/7.
17. The given points (-8, 8) and (-5, 2) have different x-coordinates and different y-coordinates. Using the slope formula, we find slope = (2 - 8) / (-5 - (-8)) = -6 / 3 = -2.
18. The given points (-3, -7) and (9, -7) have the same y-coordinate but different x-coordinates. Using the slope formula, we find the slope = (-7 - (-7)) / (9 - (-3)) = 0 / 12 = 0.
19. To write the equation of a line in point-slope form using the given conditions (slope = 4, passing through (-3, 7)), we use the formula: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Substituting the values, we get y - 7 = 4(x - (-3)).
20. The given conditions state that the slope is missing, so the equation cannot be written in point-slope form without knowing the slope.