Question

How do you find the Y intercept of an exponential form \[q\left( x \right)=-{{7}^{x-4}}-1\] ?

Answer 1

Hint: We can solve this question using the concept of X and Y intercepts of graph. To find the Y intercept we will substitute \[0\] in place of x. After that we have to perform the required arithmetic operations and calculations to arrive at the solution.

Complete step-by-step answer:
The intercepts of a graph are points at which the graph crosses the axes. The x-intercept is the point at which the graph crosses the x-axis. At this point, the y-coordinate is zero. The y-intercept is the point at which the graph crosses the y-axis. At this point, the x-coordinate is zero.
To find the x-intercept, we will put \[y=0\] and solve for x. similarly to find the y-intercept we will put \[x=0\] and solve for y. like this we can get the x and y intercepts of the exponential form.

Given equation is
\[q\left( x \right)=-{{7}^{x-4}}-1\]
To get the y-intercept of the equation we have to substitute \[x=0\] as discussed before.
After substituting x with \[0\] the equation will look like
\[\Rightarrow q\left( 0 \right)=-{{7}^{0-4}}-1\]
Now we have solved the RHS to get the value.
First we have to solve the power of \[7\]. We will get
\[\Rightarrow q\left( 0 \right)=-{{7}^{-4}}-1\]
We can observe negative power to \[7\].
 We have a formula
\[{{x}^{-a}}=\dfrac{1}{{{x}^{a}}}\]
By using this formula we can write \[{{7}^{-4}}\] as \[\dfrac{1}{{{7}^{4}}}\] .
\[\Rightarrow {{7}^{-4}}=\dfrac{1}{{{7}^{4}}}\]
After substituting this value the equation will look like
\[\Rightarrow q\left( 0 \right)=-\dfrac{1}{{{7}^{4}}}-1\]
Now we have found the value of \[{{7}^{4}}\] and have to apply required arithmetic operations to get the answer.
\[\Rightarrow {{7}^{4}}=2401\]
Then the equation will be like
\[\Rightarrow q\left( 0 \right)=-\dfrac{1}{2401}-1\]
Now we have to add both terms on the RHS side because we already know that we have added the terms which contain the same sign. So we have added both the terms.
Then the LHS will be like
\[\Rightarrow -\dfrac{1}{2401}-\dfrac{2401}{2401}\]
\[\Rightarrow -\dfrac{2402}{2401}\]
\[\Rightarrow -1.00041649\]
Then the equation will become like this
\[q\left( 0 \right)\Rightarrow -1.00041649\]
From this we can say that the y intercept of the given exponential form is \[-1.00041649\].

Note: This question can also be asked in many different ways. If it is asked to find roots , zeroes or asked to solve the particular equation we have found the intercepts only. These are different ways to ask a question. These intercepts are mainly used to draw a graph.