Math / Algebra

QuestionThe graph of $y=f(x)$ is shown below. What are all of the real solutions of $f(x)=0$ ?

Studdy Solution

STEP 1

What is this asking? Where does this graph touch the x-axis? Watch out! Don't mix up the x-axis and the y-axis!
We're looking for where the graph crosses the horizontal line, not the vertical one.

STEP 2

1. Find the x-intercepts

STEP 3

Alright, so we're looking for the solutions to $f(x) = 0$ .
What does that actually mean?
It means we're hunting for the values of $x$ where the function's value is zero.

STEP 4

Think of it like this: the function $f(x)$ tells us the height of the graph at any given $x$ value.
So, when $f(x) = 0$ , the height is zero.
And where's the height zero on a graph?
Right there on the x-axis!

STEP 5

So, we're really just looking for the places where the graph intersects the x-axis.
These are called the x-intercepts!

STEP 6

Let's look closely at the graph.
It crosses the x-axis at a few different points.
We can see one around $x = -5$ , another near $x = -2$ , and a third around $x = 3$ .

STEP 7

The solutions to $f(x) = 0$ are approximately $x = -5$ , $x = -2$ , and $x = 3$ .
Boom!

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QuestionThe graph of $y=f(x)$ is shown below. What are all of the real solutions of $f(x)=0$ ?

Studdy Solution

STEP 1

What is this asking? Where does this graph touch the x-axis? Watch out! Don't mix up the x-axis and the y-axis!
We're looking for where the graph crosses the horizontal line, not the vertical one.

STEP 2

1. Find the x-intercepts

STEP 3

Alright, so we're looking for the solutions to $f(x) = 0$ .
What does that actually mean?
It means we're hunting for the values of $x$ where the function's value is zero.

STEP 4

Think of it like this: the function $f(x)$ tells us the height of the graph at any given $x$ value.
So, when $f(x) = 0$ , the height is zero.
And where's the height zero on a graph?
Right there on the x-axis!

STEP 5

So, we're really just looking for the places where the graph intersects the x-axis.
These are called the x-intercepts!

STEP 6

Let's look closely at the graph.
It crosses the x-axis at a few different points.
We can see one around $x = -5$ , another near $x = -2$ , and a third around $x = 3$ .

STEP 7

The solutions to $f(x) = 0$ are approximately $x = -5$ , $x = -2$ , and $x = 3$ .
Boom!

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QuestionThe graph of y=f(x)y=f(x)y=f(x) is shown below. What are all of the real solutions of f(x)=0f(x)=0f(x)=0 ?

Studdy Solution

STEP 1

What is this asking? Where does this graph touch the x-axis? Watch out! Don't mix up the x-axis and the y-axis!We're looking for where the graph crosses the *horizontal* line, not the vertical one.

STEP 2

1. Find the x-intercepts

STEP 3

Alright, so we're looking for the **solutions** to f(x)=0f(x) = 0f(x)=0.What does that *actually* mean?It means we're hunting for the values of xxx where the function's value is **zero**.

STEP 4

Think of it like this: the function f(x)f(x)f(x) tells us the *height* of the graph at any given xxx value.So, when f(x)=0f(x) = 0f(x)=0, the height is zero.And where's the height zero on a graph?Right there on the **x-axis**!

STEP 5

So, we're really just looking for the places where the graph *intersects* the x-axis.These are called the **x-intercepts**!

STEP 6

Let's look closely at the graph.It crosses the x-axis at a few different points.We can see one around x=−5x = -5x=−5, another near x=−2x = -2x=−2, and a third around x=3x = 3x=3.

STEP 7

The solutions to f(x)=0f(x) = 0f(x)=0 are approximately x=−5x = -5x=−5, x=−2x = -2x=−2, and x=3x = 3x=3.Boom!

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionThe graph of $y=f(x)$ is shown below. What are all of the real solutions of $f(x)=0$ ?

What is this asking? Where does this graph touch the x-axis? Watch out! Don't mix up the x-axis and the y-axis!
We're looking for where the graph crosses the horizontal line, not the vertical one.

Alright, so we're looking for the solutions to $f(x) = 0$ .
What does that actually mean?
It means we're hunting for the values of $x$ where the function's value is zero.

Think of it like this: the function $f(x)$ tells us the height of the graph at any given $x$ value.
So, when $f(x) = 0$ , the height is zero.
And where's the height zero on a graph?
Right there on the x-axis!

So, we're really just looking for the places where the graph intersects the x-axis.
These are called the x-intercepts!

Let's look closely at the graph.
It crosses the x-axis at a few different points.
We can see one around $x = -5$ , another near $x = -2$ , and a third around $x = 3$ .

The solutions to $f(x) = 0$ are approximately $x = -5$ , $x = -2$ , and $x = 3$ .
Boom!