HOW TO FIND CHARACTERSTICS OF GRAPHS

Domain :

How the graph is spread on the x-axis is domain. In other words, for the set of x values for which it is spreading horizontally, that is known as domain.

Range :

How the graph is spread on the y-axis is range. In other words, for the set of y-values for which it is spreading vertically, that is known as range.

Maximum or minimum :

The point where the graph reaches its maximum height is maximum. When the curve changes its direction from increasing to decreasing, there will be a maximum point.

The point where the graph reaches its minimum height is minimum. When the curve changes its direction from decreasing to increasing, there will be a minimum point.

x and y intercepts :

The curve where it cuts the x-axis is known as x-intercept, the curve where it cuts the y-axis is known as y-intercept.

How to check if it is discreate or continuous ?

Discrete functions have scatter plots as graphs and continuous functions have lines or curves as graphs.

Problem 1 :

Use the graphs to state the various features.

i) Domain

ii) Range

iii) Maximum

iv) Minimum

v) Discrete or Continuous?

vi) y – intercept:

vii) x – intercept:

viii) 7𝑓(5)=

Solution :

i) Domain: (-5, 5]

ii) Range : [-4, 4]

iii) Maximum: y = 4

iv) Minimum: y = -4

v) Discrete or Continuous?

Continuous

vi) y – intercept:

y = 0

vii) x – intercept:

x = 0 and x = 5

viii) 7 𝑓(5) = 0

Problem 2 :

i) Domain:

ii) Range:

iii) Maximum:

iv) Minimum:

v) Interval of Increase:

vi) Interval of Decrease:

vii) 𝑓(2) + 𝑓(9) =

Solution :

i) Domain : [0, 12]

ii) Range: [0, 8]

iii) Maximum: y = 8

iv) Minimum: y = 0

v) Interval of Increase: (0, 3)

vi) Interval of Decrease: (9, 12)

vii) 𝑓(2) = 4 and 𝑓(9) = 8

f(2) + f(9) = 4 + 8 ==> 12

Problem 3 :

i) Domain

ii) Increasing

iii) Range

iv) Decreasing

v) x-intercept (s)

vi) Positive

vii) y-intercept

viii) Negative

ix) Maximum

x) Minimum

xi) End behaviour

Solution :

Domain

Increasing

Range

Decreasing

x-intercept(s)

Positive

y-intercept

Negative

Maximum

Minimum

[-3, 14]

(-3, 9) ꓴ (11, 14)

[-5, 10]

(9,14)

(4.5,0)

(4.5,14]

(0,-3)

[-3,4.5)

(9,10)

(-3,-5)

End Behavior: 𝑎𝑠 x → −3, y → −5; 𝑎𝑠 x → 14, y → 10

Problem 4 :

i) Domain

ii) Range

iii) x-intercept(s)

iv) y-intercept

v) Maximum

vi) Increasing

vii) Decreasing

viii) Positive

ix) Negative

x) Minimum

xi) End behaviors

Solution :

Domain

Increasing

Range

Decreasing

x-intercept(s)

Positive

y-intercept

Negative

Maximum

Minimum

End Behavior

(-∞, ∞)

(-2,-0.5) ꓴ (1, ∞)

(0, ∞)

(-∞,-2) ꓴ (-0.5,1)

(-2,0) & (1,0)

(-∞,-2) ꓴ (-2,1) ꓴ(1, ∞)

(0,4)

none

(-0.5,5.063)

(-2,0) & (1,0)

x → −∞, y → +∞; 𝑎𝑠 x → +∞, y → +∞

Problem 5 :

i) Domain

ii) Increasing

iii) Range

iv) Decreasing

v) x-intercept(s)

vi) Positive

vii) y-intercept

viii) Maximum

ix) Minimum

x) End behavior

Solution :

i) Domain

ii) Increasing

iii) Range

iv) Decreasing

v) x-intercept(s)

vi) Positive

vii) y-intercept

viii) Maximum

ix) Minimum

x) End behavior

(-∞, ∞)

(2, ∞)

(1, ∞)

(-∞,2)

none

(-∞, ∞)

(0,5)

none

(2,1)

x → −∞, y → +∞; 𝑎𝑠 x → +∞, y → +∞

HOW TO FIND CHARACTERSTICS OF GRAPHS

Recent Articles

Finding Range of Values Inequality Problems

Solving Two Step Inequality Word Problems

Exponential Function Context and Data Modeling