Answer:
a.) x ≤ 5 or (-∞,5]
b.) x ≤ 3 or (-∞,3]
c.) x = -1 & 5
d.) 1
e.) x ≤ 2 or (-∞,2]
f.) 2 < x ≤ 5 or (2,5]
g.) -1 < x < 5 or (-1,5)
h.) x = 2
i.) x = 2
j.) positive
Step-by-step explanation:
a.) Domain is every value of x on the x-axis that a function exists on so because the graph shows the function existing on and to the left of x = 5, the domain is x ≤ 5 or (-∞,5] (note the closed interval on 5 because on the graph f(5) is a closed circle).
b.) Range is every value of y on the y-axis that a function exists on so because the graph shows the highest y-value being y = 3, the range is y ≤ 3 or (-∞,3] (note again the closed interval because the graph seems to reach y = 3).
c.) The zeros of a function are the places where y = 0 so the zeros are x = -1 & 5.
d.) f(4.5) is the y-value at the x-value of 4.5. f(4.5) = 1.
A function increases when the slope is positive (when the function going up) and decreases when the slope is negative (when it's going down).
e.) f is increasing on x ≤ 2 or (-∞,2).
f.) f is decreasing on 2 < x ≤ 5 or (2,5].
g.) f(x) is less than zero when it is below the x-axis so f(x) ≤ 0 on -1 < x < 5 or (-1,5).
h.) Relative maxima and minima are where the graph has a maximum or minimum y-value (basically where it looks like a hill or a canyon). There's a relative maximum (hill) at x = 2.
i.) f(x) = 3 means the x-values where y = 3 so f(x) = 3 at x = 2.
j.) f(3) is where x = 3 on the graph. At x = 3, y ≈ 2.5 so f(3) is positive.
