Questions: Graph. f(x) = 3/2 x

Graph. f(x) = 3/2 x
Transcript text: Graph. \[ f(x)=\frac{3}{2} x \]
failed

Solution

failed
failed

Solution Steps

Step 1: Identify the Function Type

The given function is \( f(x) = \left(\frac{3}{2}\right)^x \). This is an exponential function of the form \( f(x) = a^x \), where \( a = \frac{3}{2} \).

Step 2: Determine Key Points

To graph the function, determine key points by substituting different values of \( x \):

  • For \( x = -2 \): \( f(-2) = \left(\frac{3}{2}\right)^{-2} = \left(\frac{2}{3}\right)^2 = \frac{4}{9} \approx 0.44 \)
  • For \( x = -1 \): \( f(-1) = \left(\frac{3}{2}\right)^{-1} = \frac{2}{3} \approx 0.67 \)
  • For \( x = 0 \): \( f(0) = \left(\frac{3}{2}\right)^0 = 1 \)
  • For \( x = 1 \): \( f(1) = \left(\frac{3}{2}\right)^1 = \frac{3}{2} = 1.5 \)
  • For \( x = 2 \): \( f(2) = \left(\frac{3}{2}\right)^2 = \frac{9}{4} = 2.25 \)
Step 3: Plot the Points

Plot the points on the graph:

  • \((-2, 0.44)\)
  • \((-1, 0.67)\)
  • \((0, 1)\)
  • \((1, 1.5)\)
  • \((2, 2.25)\)
Step 4: Draw the Exponential Curve

Connect the plotted points with a smooth curve to represent the exponential growth of the function \( f(x) = \left(\frac{3}{2}\right)^x \).

Final Answer

The graph of the function \( f(x) = \left(\frac{3}{2}\right)^x \) is an exponential curve that passes through the points \((-2, 0.44)\), \((-1, 0.67)\), \((0, 1)\), \((1, 1.5)\), and \((2, 2.25)\). The curve increases rapidly as \( x \) increases.

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
A police car is speeding north with its siren blaring. The sound waves from the siren increase in frequency a north of the car. b south of the car. c in all directions around the car. d none of the above
failedAnswered
Which property of muscle gives it the ability to stretch without damage? (A) Extensibility (B) Electrical excitability (C) contractility (D) Elasticity
failedAnswered
Fill in the probability distribution table for the number of heads that occur when tossing three coins simultaneously. Event Probability 3 heads, 0 tails 2 heads, 1 tail 1 head, 2 tails 0 heads, 3 tails
failedAnswered
El encargado de bodega de la multinacional MegaSúper lleva un inventario de los artículos de línea blanca que están disponible para ofrecer a los usuarios, de tal manera de hacer los respectivos pedidos y así mantener el stock en tienda. Algunos de los datos registrados en los últimos meses se muestran a continuación: Días Disponibilidad de Productos (Stock) 6 3300 9 2400 18 1600 21 1200 32 100 Modelos predictivos Los datos observados permiten utilizar diversos modelos que permiten predecir (o estimar) la disponibilidad de productos. La expresión algebraica debe ingresarse como en el siguiente ejemplo: 23.32x+5.67 ó 3.1 x^2+4.4 x+1.2 ó 3.2 x^3+1.5 x^2- 4.4 x+12 a) En el caso de utilizar el ajuste polinómico de grado 1, responda: ¿Cuál es la expresión algebraica de dicho modelo?
failedAnswered
Question 8 4 pts Match the above sediments with the type of sedimentary rock they would form if they were lithified. Gravel [Choose ] Sand [Choose ] Silt [Choose] Clay and Silt [Choose]