Questions: f(x) = -1, x ≤ -4 2x + 2, -4 < x ≤ 0 3, x > 0

f(x) = -1, x ≤ -4 2x + 2, -4 < x ≤ 0 3, x > 0
Transcript text: 2) $f(x)=\left\{\begin{array}{ll}-1, & x \leq-4 \\ 2 x+2, & -40\end{array}\right.$
failed

Solution

failed
failed

Solution Steps

Step 1: Understanding the Piecewise Function

The given function \( f(x) \) is a piecewise function defined as: \[ f(x) = \begin{cases} -1, & x \leq -4 \\ 2x + 2, & -4 < x \leq 0 \\ 3, & x > 0 \end{cases} \]

Step 2: Plotting the First Piece

For \( x \leq -4 \), \( f(x) = -1 \). This is a horizontal line at \( y = -1 \) for all \( x \leq -4 \).

Step 3: Plotting the Second Piece

For \( -4 < x \leq 0 \), \( f(x) = 2x + 2 \). This is a linear function with a slope of 2 and a y-intercept of 2. We need to plot this line segment from \( x = -4 \) to \( x = 0 \).

  • At \( x = -4 \), \( f(-4) = 2(-4) + 2 = -8 + 2 = -6 \).
  • At \( x = 0 \), \( f(0) = 2(0) + 2 = 2 \).
Step 4: Plotting the Third Piece

For \( x > 0 \), \( f(x) = 3 \). This is a horizontal line at \( y = 3 \) for all \( x > 0 \).

Final Answer

The graph of the piecewise function \( f(x) \) is as follows:

  1. A horizontal line at \( y = -1 \) for \( x \leq -4 \).
  2. A line segment from \( (-4, -6) \) to \( (0, 2) \).
  3. A horizontal line at \( y = 3 \) for \( x > 0 \).

Plot these pieces on the given coordinate plane to visualize the function.

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Use a combination of rules for exponents to simplify the expression. Give your answer in exponential form, using only positive exponents. k (x^(-2) y/z^(4))^(-3) (Simplify your answer. Type exponential notation using positive exponents.)
failedAnswered
Use the standard normal distribution to find P(-2.25<z<1.25). A. 0.4878 B. 0.8822 C. 0.0122 D. 0.8944
failedAnswered
Habitat restoration can restore and maintain . - the global climate - endemic species - biodiversity
failedAnswered
Representing Tenths The large grid below is the unit and each rectangle is 1/10 or one tenth of the unit Use the polygon tool to outline the area that represents 0.6 Write the fraction with a denominator of 10 that is equivalent to the shaded area. Write the word name that represents the shaded area.
failedAnswered
QUESTION 6 Suppose a blood cell with 1.2 mg / dL sodium concentration is immersed in a solution containing 2.5 mg / dL of sodium. Select the correct statement. The cell is hypotonic compared to the solution. The cell will lose water and crenulate (shrivel up). The cell is hypotonic to the solution. The cell will take on water and lyse (burst). The cell is hypertonic to the solution. The cell will lose water and crenulate (shrivel). The cell is hypotonic compared to the solution. The cell will take on water and lyse (burst).