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mathematics
precalculus 1st

Questions and Answers of Precalculus 1st

For the following exercises, solve the equations below and express the answer using set notation.3|x + 1| − 4 = 5
For the following exercises, consider the graph of f shown in Figure 15. Estimate the average rate of change from x = 1 to x = 4. 5 Figure 15 x
For the following exercises, find the domain of each function using interval notation. f(x)= Vx+4 x-4
For the following exercises, use Figure 2 to approximate the values.If f(x) = −2, then solve for x. Figure 2
For the following exercises, determine whether the relation represents y as a function of x x= V1-y²
For the following exercises, describe how the graph of the function is a transformation of the graph of the original function f. y = f(x) − 2
For the following exercises, evaluate the function f(x) = −3x2 + 2x at the given input.Write the domain of the function f(x) = √3 − x in interval notation.
Describe all numbers x that are at a distance of 1/2 from the number −4. Express this using absolute value notation.
For the following exercises, find the average rate of change of each function on the interval specified for real numbers b or h.p(x) = 3x + 4 on [2, 2 + h]
For the following exercises, evaluate the function f(x) = −3x2 + 2x at the given input.Given f(x) = 2x2 − 5x, find f(a + 1) − f(1).
Write a formula for the function obtained when the graph of f(x) = |x| is shifted down 3 units and to the right 1 unit.
For the following exercises, determine whether the functions are one-to-one. f(x) = −3x+ 5
For the following exercises, find the domain of each function using interval notation. f(x) = 5 − 2x2
For the following exercises, find f−1 (x) for each function. f (x) = x + 3
Given f(x) = 2x2 + 4x and g(x) = _ 1/2x , find f + g, f − g, fg, and f/g . Determine the domain for each function in interval notation.
For the following exercises, evaluate the function f(x) = −3x2 + 2x at the given input. x+1if-2
Describe the situation in which the distance that point x is from 10 is at least 15 units. Express this using absolute value notation.
For the following exercises, find the average rate of change of each function on the interval specified for real numbers b or h.k(x) = 4x − 2 on [3, 3 + h]
For the following exercises, determine whether the functions are one-to-one.f(x) = ∣x − 3∣
Write a formula for the function obtained when the graph of f(x) = 1/x is shifted down 4 units and to the right 3 units.
For the following exercises, determine whether the relation represents y as a function of x5x + 2y = 10
For the following exercises, find f−1 (x) for each function.f (x) = x + 5
For the following exercises, use the vertical line test to determine if the relation whose graph is provided is a function. Sund Pan in € II X
For the following exercises, use the vertical line test to determine if the relation whose graph is provided is a function. FIE ரான்மணக் பா f/ S
Find all function values f(x) such that the distance from f(x) to the value 8 is less than 0.03 units. Express this using absolute value notation.
For the following exercises, find the average rate of change of each function on the interval specified for real numbers b or h.f(x) = 2x2 + 1 on [x, x + h]
Write a formula for the function obtained when the graph of f(x) = 1/x2 is shifted up 2 units and to the left 4 units.
For the following exercises, determine whether the relation represents y as a function of xy = x2
For the following exercises, find the domain of each function using interval notation. f(x) = 3 − √ 6 − 2x
For the following exercises, find f−1 (x) for each function.f (x) = 2 − x
For the following exercises, describe how the graph of the function is a transformation of the graph of the original function f.y = f(x − 49)
For the following exercises, solve the equations below and express the answer using set notation. |x + 3| = 9
For the following exercises, find the average rate of change of each function on the interval specified for real numbers b or h.g(x) = 3x2 − 2 on [x, x + h]
Given f(x) = 3x2 and g(x) = √— x − 5 , find f + g, f − g, fg, and f/g . Determine the domain for each function in interval notation.
For the following exercises, determine whether the relation represents y as a function of x x = y2
For the following exercises, find the domain of each function using interval notation. f(x) = √ 4 − 3x
For the following exercises, find f−1 (x) for each function.f (x) = 3 − x
For the following exercises, solve the equations below and express the answer using set notation.|6 − x| = 5
For the following exercises, use the functions f(x) = 3 − 2x2 + x and g(x) = √x to find the composite functions.(g ∘ f)(x)
For the following exercises, determine whether the relation is a function.Is the graph in Figure 1 a function? Figure 1 25 -25-20-15-10-5. 5 10 15 20 25 ய: பொல். y ம.ம
When describing sets of numbers using interval notation, when do you use a parenthesis and when do you use a bracket?
When examining the formula of a function that is the result of multiple transformations, how can you tell a horizontal shift from a vertical shift?
For the following exercises, determine whether the relation is a function. {(a, b), (c, d), (e, d)}
Why does the domain differ for different functions?
For the following exercises, determine whether each of the following relations is a function.y = 2x + 8
How can you tell whether an absolute value function has two x-intercepts without graphing the function?
When examining the formula of a function that is the result of multiple transformations, how can you tell a horizontal stretch from a vertical stretch?
What is the difference between the input and the output of a function?
What is the composition of two functions, f ∘ g?
How do we determine the domain of a function defined by an equation?
For the following exercises, determine whether each of the following relations is a function.(2, 1), (3, 2), (−1, 1), (0, −2)}
If a function f is increasing on (a, b) and decreasing on (b, c), then what can be said about the local extremum of f on (a, c)?
How are the absolute maximum and minimum similar to and different from the local extrema?
When solving an absolute value function, the isolated absolute value term is equal to a negative number. What does that tell you about the graph of the absolute value function?
When examining the formula of a function that is the result of multiple transformations, how can you tell a horizontal compression from a vertical compression?
For the following exercises, determine whether the relation is a function.y2 + 4 = x, for x the independent variable and y the dependent variable
Explain why the domain of f(x) = 3√x is different from the domain of f(x) = √x.
Why does the vertical line test tell us whether the graph of a relation represents a function?
If the order is reversed when composing two functions, can the result ever be the same as the answer in the original order of the composition? If yes, give an example. If no, explain why not.
For the following exercises, evaluate the function f(x) = −3x2 + 2x at the given input.f(−2)
How does the graph of the absolute value function compare to the graph of the quadratic function, y =x2 , in terms of increasing and decreasing intervals?
How can you use the graph of an absolute value function to determine the x-values for which the function values are negative?
When examining the formula of a function that is the result of multiple transformations, how can you tell a reflection with respect to the x-axis from a reflection with respect to the y-axis?
How can you determine if a relation is a one-to-one function?
How do you find the domain for the composition of two functions, f ∘ g?
For the following exercises, evaluate the function f(x) = −3x2 + 2x at the given input.f(a)
How do you solve an absolute value inequality algebraically?
For the following exercises, find the average rate of change of each function on the interval specified for real numbers b or h.f(x) = 4x2 − 7 on [1, b]
How can you determine whether a function is odd or even from the formula of the function?
For the following exercises, evaluate the function at the indicated values: f(−3); f (2); f(−a); −f(a); f (a + h).f(x) = −2x2 + 3x
How do you graph a piecewise function?
For the following exercises, evaluate the function f(x) = −3x2 + 2x at the given input.Show that the function f(x) = −2(x − 1)2 + 3 is not one-to-one.
Why does the horizontal line test tell us whether the graph of a function is one-to-one?
How do you find the inverse of a function algebraically?
Given f(x) = x2 + 2x and g(x) = 6 − x2 , find f + g, f − g, fg, and f/g. Determine the domain for each function in interval notation.
Describe all numbers x that are at a distance of 4 from the number 8. Express this using absolute value notation.
For the following exercises, find the average rate of change of each function on the interval specified for real numbers b or h.g (x) = 2x2 − 9 on [4, b]
Write a formula for the function obtained when the graph of f(x) = √x is shifted up 1 unit and to the left 2 units.
For the following exercises, evaluate the function at the indicated values: f(−3); f (2); f(−a); −f(a); f (a + h).f (x) = 2∣3 x − 1∣
For the following exercises, find the domain of each function using interval notation. f(x) = −2x(x − 1)(x − 2)

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