Algebra1

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Algebra

Graph the function. Find the zeros of each function and the x- and y-intercepts of each

graph, if any exist. From the graph, determine the domain and range of each function, list

the intervals on which the function is increasing, decreasing or constant, and find the

relative and absolute extrema, if they exist.

f(x) = |4x|

Solution:

|

4𝑥

|

= 4𝑥, 𝑥 ≥ 0

= −4𝑥, 𝑥 < 0

So,

𝑓

(

𝑥

)

= 4𝑥, 𝑥 ≥ 0

𝑓

(

𝑥

)

= −4𝑥,𝑥 < 0

Find the zeros as:

4𝑥 = 0 → 𝑥 = 0

The x and y-intercept point is (0,0)

𝐷𝑜𝑚𝑎𝑖𝑛: (−∞, ∞)

𝑅𝑎𝑛𝑔𝑒: [0, ∞)

𝐼𝑛𝑐𝑟𝑒𝑎𝑖𝑠𝑛𝑔: (0,∞)

𝐷𝑒𝑐𝑟𝑒𝑎𝑖𝑠𝑛𝑔:(−∞, 0)

No, relative extrema. Absolute minimum is (0,0) , there is no absolute maximum

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Algebra Graph the function. Find the zeros of each function and the x- and y-intercepts of each graph, if any exist. From the graph, determine the domain and range of each function, list the intervals on which the function is increasing, decreasing or constant, and find the relative and absolute extrema, if they exist. f(x) = |4x| Solution: |4𝑥| = 4𝑥, 𝑥 ≥ 0 = −4𝑥, 𝑥 < 0 So, 𝑓(𝑥) = 4𝑥, 𝑥 ≥ 0 𝑓(𝑥) = −4𝑥, 𝑥 < 0 Find the zeros as: 4𝑥 = 0 → 𝑥 = 0 The x and y-intercept point is (0,0) 𝐷𝑜𝑚𝑎𝑖𝑛: (−∞, ∞) 𝑅𝑎𝑛𝑔𝑒: ...
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