As the function f(x) isn't mentioned here nor its graph, so, I can't help you with part 'd' of the question.
I'm assuming that the parts 'e' and 'f' are related to g(x) only, so,
(e) g(x) = log2(x + 3) - 1
And log can have only positive values, so, x + 3 must be greater than 0.
Hence, Domain = (-3, infinity)
For Range,
Value of log x goes from -infinity to infinity, so, Range of g(x) would also be (-infinity, infinity).
(f) The function is undefined at x = -3, or it becomes -infinity there.
So, the vertical asymptote is at x = -3.
(g) To find the inverse of g(x),
We need to interchange 'x' and 'y' in the given equation of g(x) and solve it for y,
x = log2(y + 3) - 1
or, y + 3 = 2x + 1
or, y = 2x + 1 - 3
Hence, g-1(x)= 2x + 1 - 3.
1.Let g(x) = log3(x +3)-1 . d. (3 pts) f(8)-3, the corresponding point on the graph of f(x)is.H...
(1 point) The graph of the function f(z-log2(z-1) can be obtained from the graph of g(x)-log2 z by one of the following actions: (a) shifting the graph of g(x) to the right 1 units; (b) shifting the graph of g(x) to the left 1 units; (c) shifting the graph of g(x) upward 1 units; (d) shifting the graph of g(x) downward 1 units Your answer is (input a, b, c, or d) 23 The domain of the function f(z) is...
can you do the odd #'s In Exercises 64 -69, sketch the graph of y g(x) by starting with the graph of y f(x) and using transformations. Track at least three points of your choice and the vertical asymptote through the transformations. State the domain and range of g. 64. f(r)=log2(x), g(x) = log2 (ar +1) 65. f(r) log (), g() log () +1 66. f() log3 (r), g(x)-log3(x - 2) 67. f(x) log(ax), g(x) 2 log(x + 20) -1...
Graph the function g(x)- log3 (x1) and give its domain and range using interval notation Domain: Range
please help! Use the given function f to answer parts (a) through (f) below. f(x) = -5+ log2(x-1) (a) Find the domain of t. The domain offis (Type your answer in interval notation.) (b) Choose the correct graph off below. ОА. ОВ. 10 Q Oc. OD Ay o a 10- 10 o Q -10 10 10 10 2 -10 10 (c) From the graph, determine the range and any asymptotes off. The range of fis (Type your answer in interval...
7. Let f(x)= log3 a and g(x) = 3" (a) Find the function fog (b) Graph f(x), g(x), and h(x) = x on the same grid.
10) Use number 9 to graph the function g (x) = 3 log3 x. Don't forget the asymptote. 10 8 y X 4 2 -10-8 -6-4 -2 2 468 10 -2 4 -6 -8 -10 CO 10) Use number 9 to graph the function g (x) = 3 log3 x. Don't forget the asymptote. 10 8 y X 4 2 -10-8 -6-4 -2 2 468 10 -2 4 -6 -8 -10 CO
21. 8 pts For the function g(x) = = 4x2-1 214x A. Find the horizontal asymptote. B. Find the vertical asymptote(s). 0. Find the x intercept(s). D. Solve g(x) <0. Use interval notation. E. Graph g(x)
show work 7) Given g x=3 and f x =logx, fill in each blank with the appropriate letter, A-D. Some letters may not be used or may be used more than once. [8 pts.) __ the domain off __the asymptote of g | A. (0,00) B. (-00,00) _ the asymptote off _the range of g C. x = 0 D. y = 0 8) Given the following piecewise function, give the coordinates of any open endpoints and any closed endpoints...
Given:1) \(g(x)=\frac{x^{2}+4 x-3}{x-3}\)(a) Find the domain of \(g(x)\) in interval notation.(b) Find the vertical asymptote.(c) Find the horizontal asymptote.(d) Find intercepts if any.Given:2) \(h(x)=\frac{8 x^{2}-10 x-3}{2 x^{2}-9 x+9}\)(a) Find the domain of \(g(x)\) in interval notation.(b) Find the vertical asymptote.(c) Find the horizontal asymptote.(d) Find intercepts if any,
Problem 4.1.38 Use the graph bellow of f(x) = e* to graph g(x) = e* - 1. 10- 9 -8 7 6 5- 4 (2,6 -7.39) f(x) = ? (-1,2-1=0.37) (-2, 6-2014) 2 (1, e 2.72) (0.1) Horizontal asymptote: y = 0 (a) Graph and write the equation(s) of the asymptote(s) of g. (b) The domain of g is (c) The range of g is