1. Determine whether the relation is a function.

{(-2, -7), (3, -5), (6, -4), (9, -6), (10, -1)}

A relation between x-elements and y-elements in which a given input produces

exactly one output value always is called function.

To check if a relation is function, given set of points, we need to check if any x-

elements occur more than once. If any x-element is repeated, it isnt a function.

In this example, no x-values are repeated. Hence it is a function.

2. Find the slope of the line that goes through the given points.

(-3, -7), (9, -7)

(-3, -7) is the first point. So, x1=-3 and y1=-7.

Similarly, (9, -7) is the second point . So x2=9 and y2=-7.

Slope: m= change in y = y2-y1

change in x x2-x1

Hence, =7(7)

9(3)=

7+7

9+3=

0

12= 0

3. Find the slope of the line that goes through the given points.

(-8, 8), (-5, 2)

(-8, 8) is the first point. So, x1=-8 and y1=8.

Similarly, (-5, 2) is the second point . So x2=-5 and y2=2.

Slope: m= change in y = y2-y1

change in x x2-x1

Hence, =28

5(8)=

6

5+8=

6

3= 2

4. Determine whether the relation is a function.

{(1, -3), (1, 1), (6, -8), (9, -3), (11, -3)}

A relation between x-elements and y-elements in which a given input produces

exactly one output value always is called function.

To check if a relation is function, given set of points, we need to check if any x-

elements occur more than once. If any x-element is repeated, it isnt a function.

In this example, the x-value 1 is repeated. Hence it is not a function.

5. Find the slope of the line that goes through the given points.

(-1, 4), (5, 4)

(-1, 4) is the first point. So, x1=-1 and y1=4.

Similarly, (5, 4) is the second point . So x2=5 and y2=4.

Slope: m= change in y = y2-y1

change in x x2-x1

Hence, =44

5(1)=

0

5+1=

0

6= 0

6. Determine whether the relation is a function.

{(-6, -9), (-2, 1), (1, -1), (7, -7)}

In this example, no x-values are repeated. Hence it is a function.

7. Evaluate the function at the given value of the independent variable and

simplify.

f(x) = 4x2 + 5x - 6; f(x - 1)

f(x) = 4x2 + 5x 6

To find f(x-1), we substitute x = x - 1

f(x-1) = 4(x-1)^2 + 5(x-1) 6

f(x-1) = 4[x^2-2x+1] + 5x-5 6 f(x-1) = 4x^2 - 8x + 4 +5x 5 -6 f(x-1) = 4x^2 - 3x - 7

8. Determine whether the equation defines y as a function of x.

x = y2

To check if the function x=y^2 defines y as a function of x, we solve the equation

for y. If more than one solution is obtained, then y is not a function of x

x=y^2

y^2=x

y=

y=+ or y=- Hence, The equation y2 = x does NOT define y as a function of x because

when we solve for y we must apply the square root property, which will

leave us with TWO solutions for y.

9. Evaluate the function at the given value of the independent variable and

simplify.

f(x) = x2 - 1; f(x - 2)

f(x)= x^2-1

f(x-2) = (x-2)^2-1 f(x-2) = (x^2-4x+4) - 1 f(x-2) = x^2 - 4x + 4 - 1 f(x-2) = x^2-4x+3

10. Determine whether the relation is a function.

{(-5, -4), (-2, 9), (-1, -2), (-1, 7)}

In this example, the x-value -1 is repeated. Hence it is not a function.

11. Determine whether the equation defines y as a function of x.

x + y = 9

To check if the function x=y^2 defines y as a function of x, we solve the equation

for y.

x + y = 9

x + y -x = 9 x y = 9 - x

Hence, as each value of x has unique corresponding y value, the equation

defines y as function of x.

12. Determine whether the relation is a function.

{(-7, -1), (-7, 2), (-1, 8), (3, 3), (10, -7)}

In this example, the x-value -7 is repeated. Hence it is not a function.

13. Determine whether the equation defines y as a function of x.

x2 + y2 = 1

To check if the function x=y^2 defines y as a function of x, we solve the equation

for y. If more than one solution is obtained, then y is not a function of x

X^2 + y^2 = 1

y^2 = 1 x^2

y=1 ^2

y=+1 ^2 or y=- 1 ^2

Hence, The equation y2 = x does NOT define y as a function of x because when we solve for y we must apply the square root property, which will

leave us with TWO solutions for y.

14. Find the slope of the line that goes through the given points.

(-2, -6), (-9, -17)

(-2, -6) is the first point. So, x1=-2 and y1=-6.

Similarly, (-9, -17) is the second point . So x2=-9 and y2=-17.

Slope: m= change in y = y2-y1

change in x x2-x1

Hence, =17(6)

9(2)=

17+6

9+2=

11

7= 11/7

15. Find the slope of the line that goes through the given points.

(-7, 6), (-7, -9)

(-7, 6) is the first point. So, x1=-7 and y1=6.

Similarly, (-7, -9) is the second point . So x2=-7 and y2=-9.

Slope: m= change in y = y2-y1

change in x x2-x1

Hence, =96

7(7)=

15

0=

The line is parallel to Y-axis.

16. Find the slope of the line that goes through the given points.

(3, -5), (-9, -8)

(3, -5) is the first point. So, x1=3 and y1=-5.

Similarly, (-9, -8) is the second point . So x2=-9 and y2=-8.

Slope: m= change in y = y2-y1

change in x x2-x1

Hence, =8(5)

93=

8+5

12=

3

12=

1

4

17. Use the given conditions to write an equation for the line in point-slope

form.

Slope = 6/7, passing through (8, 7)

The point slop form is

y-y1=m(x-x1)

Here, given m=6/7 and (x1,y1)=(8,7)

Hence, the equation in point slop form is

y - 7 = 6

7(x - 8).

18. Use the given conditions to write an equation for the line in point-slope

form.

Slope = 4, passing through (-3, 7)

The point slop form is

y-y1=m(x-x1)

Here, given m=4 and (x1,y1)=(-3,7)

Hence, the equation in point slop form is

y - 7 = 4(x (-3))

y - 7=4(x+3)

19. Evaluate the function at the given value of the independent variable and

simplify.

f(x) = -3x - 8; f(-2)

f(x) = - 3x - 8

To find f(-2), we substitute x= - 2

f(-2) = -3*(-2) - 8

f(-2) = 6 8 f(-2) = -2