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Black_prince [1.1K]
2 years ago
13

Given the exponential function

(3)^x" alt="f(x) = 9(3)^x" align="absmiddle" class="latex-formula">, what is the value of f(x) when x =-1
Mathematics
1 answer:
RSB [31]2 years ago
7 0

Answer:

f(-1) = 3

General Formulas and Concepts;

<u>Pre-Alg</u>

  • Order of Operations: BPEMDAS

Step-by-step explanation:

<u>Step 1: Define</u>

f(x) = 9(3)ˣ

x = -1

<u>Step 2: Solve</u>

  1. Substitute:                    f(-1) = 9(3)⁻¹
  2. Evaluate:                       f(-1) = 9(1/3)
  3. Multiply:                        f(-1) = 9/3
  4. Divide:                           f(-1) = 3
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Match each transformation of function f to a feature of the transformed function.
andrezito [222]

By analyzing the parent function graph, we will see that:

  • 1) m(x) = -f(x) ⇒  "function decreases as x increases"
  • 2)  h(x) = f(x) + 2 ⇒ "asymptote of y = 2"
  • 3) j(x) = f(x + 2) ⇒ "y-intercept at (0, 4)"
  • 4)  g(x) = 2*f(x)  ⇒ "y-intercept at (0, 2)"

<h3>What thing does each transformation?</h3>

Let's list each transformation and let's see which is the correct option for each one.

1) m(x) = -f(x).

This is a reflection over the x-axis, so, now the curve will open downwards. This means that now we have a decreasing function, so the correct option here is: <em>"function decreases as x increases"</em>

2) h(x) = f(x) + 2

This is a vertical translation of 2 units upwards. So it moves the whole graph 2 units upwards. Originally, you can see that in the left side we have an asymptote at y = 0, now that asymptote will be at y = 2.

So the correct option is: <em>"asymptote of y = 2.</em>

3) j(x) = f(x + 2)

This is a shift of 2 units to the left, notice that when we evaluate this in x =  0 we et:

j(0) = f(2) = 2^2 = 4

So the y-intercept os (0, 4).

4) g(x) = 2*f(x)

This is a vertical stretch of scale factor 2.

When we evaluate this in x = 0, we get:

g(0) = 2*f(1) = 2

So the y-intercept is at (0, 2).

If you want to learn more about transformations, you can read:

brainly.com/question/4289712

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2 years ago
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<h3><u>Answer</u> :</h3>

\bigstar\:\boxed{\bf{\purple{x^{\frac{m}{n}}}=\orange{(\sqrt[n]{x})^m}}}

Let's solve !

:\implies\sf\:25^{\frac{3}{2}}

:\implies\sf\:(\sqrt[2]{25})^3

:\implies\sf\:5^3

:\implies\boxed{\bf{\red{125}}}

<u>Hence, Oprion-D is correct</u> !

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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