Identify the horizontal and vertical asymptotes of the function y = -1 x - 4 , and state its range and domain.

The given function is y = - 1 x - 4 . Reciprocal functions of the form y = k x + d + c , where k , c and d are constants, will have a vertical asymptote with equation x = - d and a horizontal asymptote with equation y = c . So, y = - 1 x - 4 has the vertical asymptote with equation x = 4 and horizontal asymptote equal to y = 0 . y = - 1 x - 4 is well-defined for all values of x except at x = 4 . Domain of a function y = f ( x ) is the set of values of x at which f ( x ) is well-defined. Range of a function y = f ( x ) is the set of values of y where x ∈ domain of f ( x ) ∴ The domain of y = - 1 x - 4 is x ∈ ℝ , x ≠ 4 and the range is y ∈ ℝ , y ≠ 0 .

Identify the horizontal and vertical asymptotes of the function y = -1 x - 4 , and state its range and domain.

The given function is y = - 1 x - 4 . Reciprocal functions of the form y = k x + d + c , where k , c and d are constants, will have a vertical asymptote with equation x = - d and a horizontal asymptote with equation y = c . So, y = - 1 x - 4 has the vertical asymptote with equation x = 4 and horizontal asymptote equal to y = 0 . y = - 1 x - 4 is well-defined for all values of x except at x = 4 . Domain of a function y = f ( x ) is the set of values of x at which f ( x ) is well-defined. Range of a function y = f ( x ) is the set of values of y where x ∈ domain of f ( x ) ∴ The domain of y = - 1 x - 4 is x ∈ ℝ , x ≠ 4 and the range is y ∈ ℝ , y ≠ 0 .

Identify the horizontal and vertical asymptotes of the function y = 5 x + 5 , and state its range and domain.

The given function is y = 5 x + 5 . Reciprocal functions of the form y = k x + d + c , where k , c and d are constants, will have a vertical asymptote with equation x = - d and a horizontal asymptote with equation y = c . So, y = 5 x + 5 has the vertical asymptote with equation x = - 5 and horizontal asymptote equal to y = 0 . y = 5 x + 5 is well-defined for all values of x except at x = - 5 . Domain of a function y = f ( x ) is the set of values of x at which f ( x ) is well-defined. Range of a function y = f ( x ) is the set of values of y where x ∈ domain of f ( x ) ∴ The domain of y = 5 x + 5 is x ∈ ℝ , x ≠ - 5 and the range is y ∈ ℝ , y ≠ 0 .

Identify the horizontal and vertical asymptotes of the function y = 12 x + 1 + 2 , and state its range and domain.

The given function is y = 12 x + 1 + 2 . Reciprocal functions of the form y = k x + d + c , where k , c and d are constants, will have a vertical asymptote with equation x = - d and a horizontal asymptote with equation y = c . So, y = 12 x + 1 + 2 has the vertical asymptote with equation x = - 1 and horizontal asymptote equal to y = 2 . y = 12 x + 1 + 2 is well-defined for all values of x except at x = - 1 . Domain of a function y = f ( x ) is the set of values of x at which f ( x ) is well-defined. Range of a function y = f ( x ) is the set of values of y where x ∈ domain of f ( x ) ∴ The domain of y = 12 x + 1 + 2 is x ∈ ℝ , x ≠ - 1 and the range is y ∈ ℝ , y ≠ 2 .

Identify the horizontal and vertical asymptotes of the function y = 12 x + 1 - 2 , and state its range and domain.

The given function is y = 12 x + 1 - 2 . Reciprocal functions of the form y = k x + d + c , where k , c and d are constants, will have a vertical asymptote with equation x = - d and a horizontal asymptote with equation y = c . So, y = 12 x + 1 - 2 has the vertical asymptote with equation x = - 1 and horizontal asymptote equal to y = - 2 . y = 12 x + 1 - 2 is well-defined for all values of x except at x = - 1 . Domain of a function y = f ( x ) is the set of values of x at which f ( x ) is well-defined. Range of a function y = f ( x ) is the set of values of y where x ∈ domain of f ( x ) ∴ The domain of y = 12 x + 1 + 2 is x ∈ ℝ , x ≠ - 1 and the range is y ∈ ℝ , y ≠ - 2 .

Identify the horizontal and vertical asymptotes of the function y = 4 x - 3 + 2 , and state its range and domain.

The given function is y = 4 x - 3 + 2 . Reciprocal functions of the form y = k x + d + c , where k , c and d are constants, will have a vertical asymptote with equation x = - d and a horizontal asymptote with equation y = c . So, y = 4 x - 3 + 2 has the vertical asymptote with equation x = 3 and horizontal asymptote equal to y = 2 . y = 4 x - 3 + 2 is well-defined for all values of x except at x = 3 . Domain of a function y = f ( x ) is the set of values of x at which f ( x ) is well-defined. Range of a function y = f ( x ) is the set of values of y where x ∈ domain of f ( x ) ∴ The domain of y = 4 x - 3 + 2 is x ∈ ℝ , x ≠ 3 and the range is y ∈ ℝ , y ≠ 2 .

Identify the horizontal and vertical asymptotes of the function y = - 4 x - 4 - 4 , and state its range and domain.

The given function is y = - 4 x - 4 - 4 . Reciprocal functions of the form y = k x + d + c , where k , c and d are constants, will have a vertical asymptote with equation x = - d and a horizontal asymptote with equation y = c . So, y = - 4 x - 4 - 4 has the vertical asymptote with equation x = 4 and horizontal asymptote equal to y = - 4 . y = - 4 x - 4 - 4 is well-defined for all values of x except at x = 4 . Domain of a function y = f ( x ) is the set of values of x at which f ( x ) is well-defined. Range of a function y = f ( x ) is the set of values of y where x ∈ domain of f ( x ) ∴ The domain of y = - 4 x - 4 - 4 is x ∈ ℝ , x ≠ 4 and the range is y ∈ ℝ , y ≠ - 4 .

Sketch the graph of the function y = 1 x + 4 . Show the asymptotes as dotted lines and state the domain and range.

y = 1 x + 4 is the given reciprocal function. Reciprocal functions of the form y = k x + d + c , where k , c and d are constants, will have a vertical asymptote with equation x = - d and a horizontal asymptote with equation y = c . x = - 4 is the vertical asymptote and y = 0 is the horizontal asymptote of y = 1 x + 4 . x - 9 - 5 - 3 0 6 y = 1 x + 4 - 0 . 2 - 1 1 0 . 25 0 . 1 Using the above table and the equation of asymptotes, we sketch the graph of y = 1 x + 4 as follows Since, x = - 4 is the vertical asymptote of the given function, its domain is the set { x | x ∈ R \ ( - 4 ) } . Graphically we observe that the range of the function is { y | y ∈ R \ 0 } .

Sketch the graph of the function y = - 1 x + 4 . Show the asymptotes as dotted lines and state the domain and range.

y = - 1 x + 4 is the given reciprocal function. Reciprocal functions of the form y = k x + d + c , where k , c and d are constants, will have a vertical asymptote with equation x = - d and a horizontal asymptote with equation y = c . x = - 4 is the vertical asymptote and y = 0 is the horizontal asymptote of y = - 1 x + 4 . x - 9 - 5 - 3 0 6 y = - 1 x + 4 0 . 2 1 - 1 - 0 . 25 - 0 . 1 Using the above table and the equation of asymptotes, we sketch the graph of y = - 1 x + 4 as follows Since, x = - 4 is the vertical asymptote of the given function, its domain is the set { x | x ∈ R \ ( - 4 ) } . Graphically we observe that the range of the function is { y | y ∈ R \ 0 } .

Sketch the graph of the function y = 1 x + 4 + 1 . Show the asymptotes as dotted lines and state the domain and range.

y = 1 x + 4 + 1 is the given reciprocal function. Reciprocal functions of the form y = k x + d + c , where k , c and d are constants, will have a vertical asymptote with equation x = - d and a horizontal asymptote with equation y = c . x = - 4 is the vertical asymptote and y = 1 is the horizontal asymptote of y = 1 x + 4 + 1 . x - 9 - 5 - 3 0 6 y = 1 x + 4 + 1 0 . 8 0 2 1 . 25 1 . 1 Using the above table and the equation of asymptotes, we sketch the graph of y = 1 x + 4 + 1 as follows Since, x = - 4 is the vertical asymptote of the given function, its domain is the set { x | x ∈ R \ ( - 4 ) } . Graphically we observe that the range of the function is { y | y ∈ R \ 1 } .