Graph1
Domain: (-∞ to ∞).
Range: (-∞ to 0)
End behavior:As x → +∞, f(x) → -∞
As x → -∞, f(x) → -∞
Increases: -∞ to 1
Decreases: 1 to +∞
x-intercept: 1
y-intercept: -5
Graph2
Domain: (-∞ to ∞).
Range: (-9 to +∞ )
End behavior: As x → +∞, f(x)→ +∞
As x → -∞, f(x) → -∞
Increases: -∞ to 0
Decreases: 0 to +∞
x-intercepts: -3 and 3
y-intercept: -9
How to determine domain and range of function.
Domain: set of input values in a function. Range: set of output values. Both define the function's scope and potential outcomes.
End behavior describes how a function behaves as the input approaches positive or negative infinity, revealing long-term trends.
For graph 1
Domain: The curve opens infinitely downard in both directions. so, domain all real numbers.(-∞ to ∞).
Range: From -∞ to 0. Range is all negative values of y.
End behavior: As x → +∞, f(x) → -∞
As x → -∞, f(x) → -∞
As x increases from both ends f(x) goes infinitely downard.
f(x) increases from -∞ to 1 and decreases from 1 to ∞
x-intercepts is 1(where it touches the x-axis)
y-intercept is -5, where it crosses the y-axis.
For graph 2
Domain: (-∞ to ∞) since f(x) opens upwards infinitely.
Range: From -9 to +∞, f(x) opens upwards.
End behavior: As x → +∞, f(x)→ +∞
As x → -∞, f(x) → -∞
f(x) decreases from -∞ to 0 and increases from 0 to +∞
x-intercepts are -3 and 3 1(where f(x) cross the x-axis)
y-intercept is -9, where it crosses the y-axis.