Chapter 1 Test

Pg 173 #6-7 Identify the graph or graphs in which y is a function of x. (Graphs pictured)

Look at the graphs. Then take a vertical line and place it on the graph. If the graph is a function, then no matter where on the graph you place the vertical line, the graph should only cross the vertical line once.

Pg. 101 #16 Simplify the expression. (5^2 - 2^4) + [9 + (-3)]

Order of operations: PEMDAS Parenthesis Exponent Add Subtract

Pg 174 #27 Write the equation in point-slope form and slope intercept form. Passing through (6, -4) and parallel to the line whose equation is x + 2y = 5.

Parallel lines have the same slope. You have to simplify the equation to slope-intercept form y = mx + b to find the slope.

Pg 174 #25 Write the equation in point-slope form and slope intercept form. Passing through (-1,-3) and (4,2)

Point-slope form: Y−b=m(x−a) When an equation is written in this form, m gives the slope of the line and (a,b) is a point the line passes through. Slope intercept form: Y= mx + b M is slope, b is y intercept.

Pg. 101 #6 Express the interval in set builder notation and graph the interval on a number line.: [-3,2)

Set builder notation expresses all of the numbers that are included in the interval. The bracket means that the number is included, while the parenthesis means it is excluded. { x | x...}

Pg. 174 #21 Find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line rises, falls, is horizontal, or vertical. (5,2) and (1,4)

Slope = (y2 - y1)/(x2-x1) A positive slope means that the line is rising, negative means it is falling, slope of zero means it is horizontal, undefined slope is vertical.

Pg. 101 #2 Evaluate 8 + 2(x-7)^4, for x=10.

Substitute 10 for x: 8 + 2(10-7)^4. Simplify within the parenthesis: 8 + 2(3)^4 Exponent: 8 + 2(3*3*3*3) 8 + 2(81) Multiply: 8 + 162 Add: 171

Pg. 174 #13 f(x)= x^2+ 4x g(x)= x+ 2 Find: (f +g)(x) and (f+g)(3)

Substitute the equations in for f and g. (F+g)(x)= (X^2 + 4x) + (x+2) Substitute 3 for x. (F+g)(3) = [3^2+4(3)] + (3+2)

Pg. 101 #23 Solve the equation. If the solution set is (Z) or (-infinity, infinity), classify the equation as an inconsistent equation or an identity. 3(2x - 4) = 9 - 3(x + 1)

A consistent system of equations has at least one solution, and an inconsistent system has no solution. An identity is an equation that is always true no matter the value of the variable. Divide each side by 3. 2x-4 = 3-x-1 Simplify. 2x-4=2-x Add 4 to both sides, add x to both sides. 3x = 6 Divide each side by 3. X= 2

Pg 101 #24 Solve the equation. If the solution set is (Z) or (-infinity, infinity), classify the equation as an inconsistent equation or an identity. (2x-3)/4 = (x-4)/2 - (x+1)/4

A consistent system of equations has at least one solution, and an inconsistent system has no solution. An identity is an equation that is always true no matter the value of the variable. Multiply by the least common denominator, 4. 2x-3 = 2(x-4) - (x+1) Distribute 2x-3 = 2x-8 -x-1 Simplify 2x-3 = x-9 Add 3 to both sides, add x to both sides. X=-6

Pg. 101 #25 Solve the equation. If the solution set is (Z) or (-infinity, infinity), classify the equation as an inconsistent equation or an identity. 3(x-4) + x = 2(6+ 2x)

Distribute the number that is outside of the parenthesis. 3x-12+x = 12+4x Add 12 to both sides. 4x = 24 +4x Subtract 4x from both sides. 0 = 24 Inconsistent equation, it has no solution.

Pg 173 #4 Determine whether each relation is a function. Give the domain and range for each relation. If f(x) = 3x-2, find f(a+4)

Functions are relations that derive one output for each input, or one y-value for any x-value inserted into the equation. For example, the equations y = x + 3 and y = x2 - 1 are functions because every x-value produces a different y-value. In graphical terms, a function is a relation where the first numbers in the ordered pair have one and only one value as its second number, the other part of the ordered pair.

Pg. 101 #29 Use the five step strategy for solving word problems. After a 60% reduction, a jacket sold for $20. What was the jacket's price before the reduction?

Identify the problem, gather information, create an equation, solve the problem, verify the answer. Let x = price of jacket before reduction X-.6x = 20 Solve for x

Pg 101 #26 Use the five step strategy for solving word problems. Find two numbers such that the second number is 3 more than twice the first number and the sum of the two numbers is 72.

Identify the problem, gather information, create an equation, solve the problem, verify the answer. Y = 3 + 2x x + y = 72 Substitute 3 + 2x for y. X + (3+2x) = 72 Simplify 3x + 3 = 72 Subtract 3 from both sides. 3x=69 Divide by 3 on both sides. X=23