Questions: Graph this function. f(x)= x+5 if x<1 6x-12 if x ≥ 1

Graph this function. f(x)= x+5 if x<1 6x-12 if x ≥ 1
Transcript text: Graph this function. \[ f(x)=\left\{\begin{array}{ll} x+5 & \text { if } x<1 \\ 6 x-12 & \text { if } x \geq 1 \end{array}\right. \]
failed

Solution

failed
failed

Solution Steps

Step 1: Analyze the first equation

The first equation is f(x) = x + 5 if x < 1. We need two points to graph this. Let's choose x = 0 and x = -1.

If x = 0, f(x) = 0 + 5 = 5. This gives the point (0, 5). If x = -1, f(x) = -1 + 5 = 4. This gives the point (-1, 4).

Since x is strictly less than 1, there will be an open circle at x = 1. When x = 1, f(x) = 1 + 5 = 6. Thus, there's an open circle at (1, 6).

Step 2: Analyze the second equation

The second equation is f(x) = 6x - 12 if x ≥ 1. Let's choose x = 1 and x = 2.

If x = 1, f(x) = 6(1) - 12 = 6 - 12 = -6. This gives the point (1, -6). If x = 2, f(x) = 6(2) - 12 = 12 - 12 = 0. This gives the point (2, 0).

Since x is greater than or equal to 1, there will be a closed circle at x = 1.

Final Answer:

The graph will consist of two lines.

The first line segment starts at (1,6) with an open circle and passes through (0,5) and (-1,4), extending to negative infinity.

The second line segment starts at (1,-6) with a closed circle and passes through (2,0), extending to positive infinity.

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Which of the following partial order diagrams is the correct diagram for the divisor order on D24 := 1, 2, 3, 4, 6, 8, 12, 24 ordered by divisibility?
failedAnswered
A typical population curve is shown in the figure. The population is small at t=0 and increases toward a steady-state level called the carrying capacity. The population of a species is given by the function P(t) = K t² / (t² + b), where t ≥ 0 is measured in years and K and b are positive real numbers. Complete parts (a) through (c) below. a. With K=500 and b=18, what is lim t→∞ P(t), the carrying capacity of the population? lim t→∞ P(t) = (Simplify your answer.) b. With K=500 and b=18, when does the maximum growth rate occur? The maximum growth rate occurs at t= . (Type an exact answer, using radicals as needed.) c. For arbitrary values of K and b, when does the maximum growth rate occur (in terms of K and b)? The maximum growth rate occurs at t= . (Type an exact answer, using radicals as needed.)
failedAnswered
∫ from -1 to 0 of x/(x²+1) dx
failedAnswered
Gegeben ist die Funktion f: R → R, f(x) = √x. Bestimmen Sie den Definitionsbereich der Funktion f.
failedAnswered
For the following data set: (a) Compute the least-squares regression line. Round the answers to at least four decimal places. Regression line equation: (b) Which point is an outlier?