section 1.3 more on functions and their graphs 197\nwhere\n52. use the graph of f to determine each of the…

section 1.3 more on functions and their graphs 197\nwhere\n52. use the graph of f to determine each of the following. where applicable, use interval notation.\na. the domain of f\nb. the range of f\nc. the zeros of f\nd. f(0)\ne. intervals on which f is increasing\nf. intervals on which f is decreasing\ng. intervals on which f is constant\nh. values of x for which f(x)>0\ni. values of x for which f(x)= - 2\nj. is f(4) positive or negative?\nk. is f even, odd, or neither?\nl. is f(2) a relative maximum?\nin exercises 53 - 58, evaluate each piecewise function at the given values of the independent variable.\n53. f(x) = {3x + 5 if x<0; 4x + 7 if x≥0}

section 1.3 more on functions and their graphs 197\nwhere\n52. use the graph of f to determine each of the following. where applicable, use interval notation.\na. the domain of f\nb. the range of f\nc. the zeros of f\nd. f(0)\ne. intervals on which f is increasing\nf. intervals on which f is decreasing\ng. intervals on which f is constant\nh. values of x for which f(x)>0\ni. values of x for which f(x)= - 2\nj. is f(4) positive or negative?\nk. is f even, odd, or neither?\nl. is f(2) a relative maximum?\nin exercises 53 - 58, evaluate each piecewise function at the given values of the independent variable.\n53. f(x) = {3x + 5 if x<0; 4x + 7 if x≥0}

Answer

Explanation:

Step1: Identify domain from graph

Domain is the set of all x - values. From the graph, x ranges from - 5 to 5. $[-5,5]$

Step2: Identify range from graph

Range is the set of all y - values. The lowest y - value is - 3 and the highest is 2. $[-3,2]$

Step3: Find zeros of f

Zeros are x - values where y = 0. From the graph, x=-4 and x = 4. $x=-4,4$

Step4: Find f(0)

When x = 0, y = 1. $f(0)=1$

Step5: Find increasing intervals

Increasing means as x increases, y increases. The function is increasing on $[-5,-2]$. $[-5,-2]$

Step6: Find decreasing intervals

Decreasing means as x increases, y decreases. The function is decreasing on $[2,5]$. $[2,5]$

Step7: Find constant intervals

Constant means y - value does not change with x. The function is constant on $[-2,2]$. $[-2,2]$

Step8: Find x for f(x)>0

y>0 when - 4 < x < 4. $(-4,4)$

Step9: Find x for f(x)=-2

y=-2 when x=-5 and x = 5. $x=-5,5$

Step10: Determine f(4) sign

At x = 4, y = 0, so it is neither positive nor negative. Neither

Step11: Check if f is even, odd or neither

$f(-x)\neq f(x)$ and $f(-x)\neq - f(x)$, so it is neither. Neither

Step12: Check if f(2) is relative maximum

f(2) is part of a constant - value section, not a relative maximum. No

Answer:

a. $[-5,5]$ b. $[-3,2]$ c. $x=-4,4$ d. $f(0)=1$ e. $[-5,-2]$ f. $[2,5]$ g. $[-2,2]$ h. $(-4,4)$ i. $x=-5,5$ j. Neither k. Neither l. No