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Solve the inequalities.

a) |x – 1| â‰¤ 5

b) |9 – (x/-3)| > 0

Write equations of the lines through the given point parallel to and perpendicular to the given line.

4x – ?y = 3, (2,1)

Sketch the graph of the function:

f(x) = 5, x < |f(x) + 4x + 3|, x > |f(x)|

Identify the parent function f(x), describe the sequence of transformations from f(x) to g(x), and sketch the graph of g(x).

g(x) = a(x) + 3(x – 1) + 3

Find the inverse function of f(x) = 2x + 3.

Write the quadratic function in standard form and sketch the graph:

f(x) = -2x^2 + yx + 1

Find all zeros of the function and write the polynomial as the product of linear factors:

f(x) = 4x^3 + 14x^2 + 6x

Use the properties of logarithm to expand the expression:

ln(cge^m)

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02:29

1. f(x) = âˆš(2 – 3x) (x + 1)(x – 1)(a) Solve the inequality 2 – 3x < 0.(b) Solve the equation (x + 1)(x – 1) = 0.(c) What is the domain of f(x)?2. f(x) = |3x + 1|(a) Sketch a graph of the toolkit function |x|.(b) Solve the two equations: 3x + 1 = 0 and 3x + 1 = 1.(c) Use the method we learned in class to sketch a graph of f(x). Please label the y-intercept clearly.3. Let g(x) = -3x^2 + 6.*For each of the following parts, you must label the y-intercept clearly. Not, unless otherwise indicated, the x-intercept(s) if there even are any.(a) Sketch a graph of the toolkit function x^2.(b) Sketch a graph of the partially transformed function -x^2.(c) Sketch a graph of the partially transformed function -3x^2.(d) Sketch a graph of g(x) and label the x-intercept(s).

06:57

Consider the following function: f(x) = 3x^2 – 6x + 5. Answer the following questions. Is this graph concave up or concave down? What would be the equation of f(x) in standard form? Show work below. Hint: You should complete the square.What is the vertex of f(x)? Write as an ordered pair.What is the equation for the axis of symmetry of f(x)? Hint: This should be an equation, NOT a single number as it is the equation of a line.What are the y-intercepts, if any, of f(x)? If none, state “none”. Write the y-intercept as an ordered pair. Show your work.What are the x-intercepts, if any, of f(x)? If none, state “none”. Write the x-intercepts as ordered pairs. Give exact answers. Show your work.Graph f(x). Include the vertex, x-intercepts, and y-intercepts on the graph. Include additional points if needed.What is the domain of f(x) in interval notation?What is the range of f(x) in interval notation?Is the function even, odd, or neither?What interval(s) on the domain is f(x) inc…

01:44

Question 1Suppose the functions f; g; h; r and ` are deÖned as follows:f (x) = 13log314+ log3 xg (x) = q(x 3)2h (x) = 5x 2x2r (x) = 23x+1 2×2` (x) = 1px1.1 Write down Df ; the domain of f and then solve the equation f (x) = log 13p3 x: (6)1.2 Write down Dg and then solve the equation g (x) = x2: (6)1.3 Write down Dh and then solve the inequality 2 h (x): (6)1.4 Write down Dr and then solve the equation r (x) = 0: (6)1.5 Write down Dr` without Örst calculating (r `) (x): (2)1.6 Write down D`gwithout Örst calculating `g(x): (4)

04:43

Write a formula for the piecewise function graphed in the figure. You should assume that if the graph has no endpoint marked (and continues to the edge of the picture) then it continues in this fashion without end.

(a) The formula for the left piece of ?(?) is ?(?)= help (formulas) for all ? that satisfy the inequality help (inequalities)

(b) The formula for the right piece of ?(?) is ?(?)= help (formulas) for all ? that satisfy the inequality help (inequalities)

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