Question

The function f is defined as follows. f(x) = { - 3x + 4 if x < 1 2x - 1 if x ? 1 (a) Find the domain of the function. (b) Locate any intercepts. (c) Graph the function. (d) Based on the graph, find the range. (a) The domain of the function f is [ ]. (Type your answer in interval notation.)

          The function f is defined as follows.
f(x) = {
- 3x + 4 if x < 1
2x - 1 if x ? 1
(a) Find the domain of the function.
(b) Locate any intercepts.
(c) Graph the function.
(d) Based on the graph, find the range.

(a) The domain of the function f is [ ].
(Type your answer in interval notation.)
        
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The function f is defined as follows.
f(x) = 
- 3x + 4 if x < 1
2x - 1 if x ? 1
(a) Find the domain of the function.
(b) Locate any intercepts.
(c) Graph the function.
(d) Based on the graph, find the range.

(a) The domain of the function f is [ ].
(Type your answer in interval notation.)

Added by Javier J.

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Elementary and Intermediate Algebra
Elementary and Intermediate Algebra
Alan S. Tussy, R. David Gustafson 5th Edition
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The function f is defined as follows: f(x) = { -3x + 4 if x < 1 2x - 1 if x ≥ 1 (a) Find the domain of the function. (b) Locate any intercepts. (c) Graph the function. (d) Based on the graph, find the range. (a) The domain of the function f is [ ]. (Type your answer in interval notation.)
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Transcript

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00:03 Okay, in this problem, we have this piecewise function, f of x, is equal to, well, let's look at it, f of x, is equal to two different graphs at two different intervals.
00:16 So we have it's negative 3x plus four when x is less than one.
00:22 So when x is less than one.
00:24 All right.
00:25 And then we have 2x minus one when x is greater than or equal to one.
00:31 All right, so we're asked to find multiple things, but in this first problem, we're only asked to find the domain.
00:39 So the domain, what it is, is all the possible x values, all possible x values.
00:49 All possible x values.
00:52 Okay.
00:53 Now you might think this as all the possible inputs, right? the x values can also be described as the inputs, right? they can also be described as the left to right, right? on when we look at the graph, what left to right values can it take? but let's think about it with all possible x values, because we can look at this part of our piecewise function to help us think about that...
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