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USPshnik [31]
3 years ago
14

Which exponential function does not have an x-intercept? A. f(x) = 5x – 5 – 1 B. f(x) = 5x – 5 – 5 C. f(x) = -5x – 5 + 5 D. f(x)

= -5x – 5 – 1

Mathematics
2 answers:
MrRa [10]3 years ago
8 0

Answer:

Option D does not have an x-intercept. Please se attached graph

Step-by-step explanation:

To solve this equation easily, we graph each equation in a graphing calculator and see which of them doesn't intercept the x-axis.

The correct answer is option

D

f(x)  = - 5^(x-5) - 1

lys-0071 [83]3 years ago
4 0

Answer:

The correct option is (D) f(x)=-5^{x-5}-1.

Step-by-step explanation:

Consider the option A. f(x)=5^{x-5}-1

To find whether the exponential function has <em>x</em> intercepts, substitute f(x) = 0 \, \text {in} f(x)=5^{x-5}-1.

0=5^{x-5}-1

1=5^{x-5}

The above equality holds only for <em>x</em> = 5.

Now, consider the option B. f(x)=5^{x-5}-5

Similarly, substitute f(x) = 0 \, \text{in} f(x)=5^{x-5}-5

0=5^{x-5}-5

5=5^{x-5}

The above equality holds only for <em>x</em> = 6.

Consider the option C. f(x)=-5^{x-5}+5

Substitute f(x) = 0 \, \text{in} f(x)=-5^{x-5}+5

0=-5^{x-5}+5

-5=-5^{x-5}

5=5^{x-5}

The above equality holds only for <em>x</em> = 6.

Now, consider the option D. f(x)=-5^{x-5}-1

Substitute f(x) = 0 \, \text{in} f(x)=-5^{x-5}-1

0=-5^{x-5}-1

1=-5^{x-5}

This equality never holds for any real number.

We can draw the graph for the provided options with the help of graphing utility.

We can verify our result with the help of figure 1.

From the figure 1, it is clear that the graph of f(x)=-5^{x-5}-1 does not have an <em>x</em> intercept.

Hence, the correct option is (D) f(x)=-5^{x-5}-1.

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The equation of line is:

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Further explanation:

The standard form of equation in point-slope form is:

y = mx+b

Given equation is:

3x+2y=10

We have to convert it into point slope form, for which we have to isolate y on one side of equation

3x+2y = 10\\2y = -3x +10\\y = \frac{-3}{2}x + \frac{10}{2}\\y = \frac{-3}{2}x + 5

Comparing with standard form:

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As the new line is parallel to given line, their slopes will be equal

So,

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To find the value of b, putting the given point (4,-5) in equation

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Keywords: Point-slope form, equation of line

Learn more about point-slope form of equation at:

  • brainly.com/question/1577690
  • brainly.com/question/1563227

#LearnwithBrainly

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