Question

Write your answers on notebook paper. Show your work. 1. Given f(x) = x2 − 4x + 5, find each value. a. f(2) b. f(−6) 2. Find the slope and y-intercept. a. y = 3x − 4 b. 4x − 5y = 15 3. Graph each equation. a. 2x + 3y = 12 b. x = 7 4. Write an equation for each line. a. line with slope 3 and y-intercept −2 b. line passing through (2, 5) and (−4, 1) 5. Write the equation of the line below. A line with a y-intercept of 6 and a slope of negative 1 is graphed on a 4 quadrant coordinate grid. 6. Using the whole number 5, define the additive inverse and the multiplicative inverse. 7. Solve 3(x + 2) + 4 = 5x + 7. 8. What is the absolute value of 2 and of −2? Explain your response. 9. Solve the equation for x. 3x+yz=2 You Started Thursday, August 13th 2020 - 8:00 am 3 x + y = 2 z 3 x = − y + 2 z x = 2/3z - y/3 10. Which point is a solution to the equation 6x − 5y = 4? Justify your choice. (1, 2) (1, −2) (−1, −2) (−1, 2) 11. Find the domain and range of each relation. a. y = 2x + 1 b. input 3 7 11 output −1 −3 −5 c. d. Graph of a function, shaped like a curve, with a vertex on y = negative 4, on a 4 quadrant coordinate grid. 12. How many lines of symmetry exist in the figure shown in Item 11c?

Answer 1

Answer: please find the answer in the explanation

Step-by-step explanation:

Given f(x) = x2 − 4x + 5,

To find each value. a. f(2) b. f(−6) , substitute x for each value

A.) F(2) = 2^2 - 4(2) + 5

F(2) = 4 - 8 + 5 = 1

B.) F(-6) = (-6)^2 - 4(-6) + 5

F(-6) = 36 + 24 + 5 = 65

2.) Find the slope and y-intercept.

a. y = 3x − 4

Slope = 3 and intercept = -4

b. 4x − 5y = 15 

First rearrange

-5y = -4x + 15

Y = 4/5 x - 3

Slope = 4/5 and intercept = 3

4. Write an equation for each line. a. line with slope 3 and y-intercept −2 b. line passing through (2, 5) and (−4, 1)

Given that x = 2 and y = 5

3 = (y - 5)/( x - 2)

Cross multiply

3x - 6 = y - 5

Y = 3x - 1

Also, given that x = -4 and y = 1

Repeat the same process

3 = (y - 1)/(x + 4)

3x + 12 = y - 1

Y = 3x + 13

5. Write the equation of the line below. A line with a y-intercept of 6 and a slope of negative 1 is graphed on a 4 quadrant coordinate grid.

The equation will be:

Y = -x - 6

6. Using the whole number 5, define the additive inverse and the multiplicative inverse.

Additive inverse of 5 = -5

Multiplicative inverse of 5 = 1/5

7. Solve 3(x + 2) + 4 = 5x + 7.

Open the bracket

3x + 10 = 5x + 7

Collect the like terms

2x = 3

X = 3/2

8. What is the absolute value of 2 and of −2? Explain your response. 

Absolute value of any number is always positive. The answer to both questions is 2

11. Find the domain and range of each relation. a. y = 2x + 1

Domain: x = all real numbers

Range: y = all real numbers

b. input 3 7 11 output −1 −3 −5 c. d. Graph of a function, shaped like a curve, with a vertex on y = negative 4, on a 4 quadrant coordinate grid. 12. How many lines of symmetry exist in the figure shown in Item 11c?